An Introduction to Logarithmic Functions

>> DOWNLOAD LINK 🎞️ #1 <<

>> DOWNLOAD LINK 🎞️ #2 <<

>> COPY / PASTE LINK PLEASE 🎵 MP3 <<

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=EvQCLCaiq2U

From Thinkwell's College Algebra • Chapter 6 Exponential and Logarithmic Functions, Subchapter 6.2 Logarithmic Functions","styleRuns":[{"startIndex":0,"length":118,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":118,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CLYBELsvGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC0V2UUNMQ2FpcTJVGAYyJSIRIgtFdlFDTENhaXEyVTAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CLYBELsvGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CLUBELovIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"ys9fgkjFs_c","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/ys9fgkjFs_c/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBeqr5txrrwCcKlyhC7dPNuHYY0fg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/ys9fgkjFs_c/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLB2M4JjfTCwyhYTkv7pH4xBXA-rVQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Converting between Exponential and Logarithmic Functions, Part 1 by ThinkwellVids 30,844 views 10 years ago 1 minute, 4 seconds"}},"simpleText":"Converting between Exponential and Logarithmic Functions, Part 1"},"longBylineText":{"runs":[{"text":"ThinkwellVids","navigationEndpoint":{"clickTrackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@ThinkwellVids","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCKSw2beFBFAuB4RP2i5DZ2g","canonicalBaseUrl":"/@ThinkwellVids"}}}]},"publishedTimeText":{"simpleText":"10 years ago"},"viewCountText":{"simpleText":"30,844 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"1 minute, 4 seconds"}},"simpleText":"1:04"},"navigationEndpoint":{"clickTrackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=ys9fgkjFs_c","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"ys9fgkjFs_c","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=cacf5f8248c5b3f7 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1411250 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"ThinkwellVids","navigationEndpoint":{"clickTrackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@ThinkwellVids","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCKSw2beFBFAuB4RP2i5DZ2g","canonicalBaseUrl":"/@ThinkwellVids"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_ke7JZkeXKFytllEihO_YQRzyaspoRIh_YN4fdP3W5d3Rk=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLchA9-eWxqTw1-fKAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"30K views"}},"simpleText":"30K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLMBEP6YBBgFIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLMBEP6YBBgFIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"ys9fgkjFs_c","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLMBEP6YBBgFIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["ys9fgkjFs_c"],"params":"CAQ%3D"}},"videoIds":["ys9fgkjFs_c"]}},{"clickTrackingParams":"CLMBEP6YBBgFIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLQBELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CLMBEP6YBBgFIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt5czlmZ2tqRnNfYw%3D%3D","commands":[{"clickTrackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLIBEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CK8BEKQwGAAiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"1 minute, 4 seconds"}},"simpleText":"1:04"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLEBEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"ys9fgkjFs_c","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLEBEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"ys9fgkjFs_c"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLEBEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLABEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLABEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"ys9fgkjFs_c","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLABEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["ys9fgkjFs_c"],"params":"CAQ%3D"}},"videoIds":["ys9fgkjFs_c"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLABEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Converting between Exponential and Logarithmic Functions, Part 1 - 1 minute, 4 seconds - Go to channel - ThinkwellVids - 30K views - 10 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"kaga-7Y44qc","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/kaga-7Y44qc/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-BIAC4AOKAgwIABABGF8gTChlMA8= rs=AOn4CLAgT2I_uKlq4BlnD7xLEpzzz9BQPw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/kaga-7Y44qc/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gSAAuADigIMCAAQARhfIEwoZTAP rs=AOn4CLDdv2qxdIZS6mytYTMZ9_Zj56x7kg","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Solving Logarithmic Equations by ThinkwellVids 790,783 views 10 years ago 12 minutes, 54 seconds"}},"simpleText":"Solving Logarithmic Equations"},"longBylineText":{"runs":[{"text":"ThinkwellVids","navigationEndpoint":{"clickTrackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@ThinkwellVids","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCKSw2beFBFAuB4RP2i5DZ2g","canonicalBaseUrl":"/@ThinkwellVids"}}}]},"publishedTimeText":{"simpleText":"10 years ago"},"viewCountText":{"simpleText":"790,783 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"12 minutes, 54 seconds"}},"simpleText":"12:54"},"navigationEndpoint":{"clickTrackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=kaga-7Y44qc","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"kaga-7Y44qc","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=91a81afbb638e2a7 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2268750 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"ThinkwellVids","navigationEndpoint":{"clickTrackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@ThinkwellVids","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCKSw2beFBFAuB4RP2i5DZ2g","canonicalBaseUrl":"/@ThinkwellVids"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_ke7JZkeXKFytllEihO_YQRzyaspoRIh_YN4fdP3W5d3Rk=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLchAp8XjsbvfhtSRAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"790K views"}},"simpleText":"790K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CK0BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CK0BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"kaga-7Y44qc","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CK0BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["kaga-7Y44qc"],"params":"CAQ%3D"}},"videoIds":["kaga-7Y44qc"]}},{"clickTrackingParams":"CK0BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CK4BELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CK0BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtrYWdhLTdZNDRxYw%3D%3D","commands":[{"clickTrackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKwBEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CKkBEKQwGAEiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"12 minutes, 54 seconds"}},"simpleText":"12:54"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKsBEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"kaga-7Y44qc","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKsBEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"kaga-7Y44qc"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKsBEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKoBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKoBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"kaga-7Y44qc","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKoBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["kaga-7Y44qc"],"params":"CAQ%3D"}},"videoIds":["kaga-7Y44qc"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKoBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Solving Logarithmic Equations - 12 minutes, 54 seconds - Go to channel - ThinkwellVids - 790K views - 10 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/kaga-7Y44qc/mqdefault_6s.webp?du=3000 sqp=CKu65L0G rs=AOn4CLCT3jmLYAX3QyFAGYIgLPm6PmhdlA","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"LRbi_pMX1DM","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/LRbi_pMX1DM/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCvGjsgtGMLXuvq8llCumKYyRkB9w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/LRbi_pMX1DM/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCIqyjGZP7XiG55osrLBz1lryuJcQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Logarithms Explained Rules Properties, Condense, Expand, Graphing Solving Equations Introduction by The Organic Chemistry Tutor 2,005,847 views 8 years ago 1 hour, 23 minutes"}},"simpleText":"Logarithms Explained Rules Properties, Condense, Expand, Graphing Solving Equations Introduction"},"longBylineText":{"runs":[{"text":"The Organic Chemistry Tutor","navigationEndpoint":{"clickTrackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@TheOrganicChemistryTutor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEWpbFLzoYGPfuWUMFPSaoA","canonicalBaseUrl":"/@TheOrganicChemistryTutor"}}}]},"publishedTimeText":{"simpleText":"8 years ago"},"viewCountText":{"simpleText":"2,005,847 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"1 hour, 23 minutes, 53 seconds"}},"simpleText":"1:23:53"},"navigationEndpoint":{"clickTrackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=LRbi_pMX1DM","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"LRbi_pMX1DM","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=2d16e2fe9317d433 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2268750 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"The Organic Chemistry Tutor","navigationEndpoint":{"clickTrackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@TheOrganicChemistryTutor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEWpbFLzoYGPfuWUMFPSaoA","canonicalBaseUrl":"/@TheOrganicChemistryTutor"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lOQikQsmqQS3dG9VBvbJ03Eqqw7NshUvDNorj5UAZL6M0=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLchAs6jfmOnfuIst","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"2 million views"}},"simpleText":"2M views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKcBEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKcBEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"LRbi_pMX1DM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKcBEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["LRbi_pMX1DM"],"params":"CAQ%3D"}},"videoIds":["LRbi_pMX1DM"]}},{"clickTrackingParams":"CKcBEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CKgBELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CKcBEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtMUmJpX3BNWDFETQ%3D%3D","commands":[{"clickTrackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKYBEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CKMBEKQwGAIiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"1 hour, 23 minutes, 53 seconds"}},"simpleText":"1:23:53"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKUBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"LRbi_pMX1DM","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKUBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"LRbi_pMX1DM"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKUBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKQBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKQBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"LRbi_pMX1DM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKQBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["LRbi_pMX1DM"],"params":"CAQ%3D"}},"videoIds":["LRbi_pMX1DM"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKQBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Logarithms Explained Rules Properties, Condense, Expand, Graphing Solving Equations Introduction - 1 hour, 23 minutes - Go to channel - The Organic Chemistry Tutor - 2M views - 8 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"ntBWrcbAhaY","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/ntBWrcbAhaY/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBScmPDXHQoQsetliiD1RiYQdAHqQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/ntBWrcbAhaY/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDuQGnJ6aVskFfjuH7_6d-e1JGL9g","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Introduction to Logarithms (1 of 2: Definition) by Eddie Woo 1,431,537 views 7 years ago 7 minutes, 53 seconds"}},"simpleText":"Introduction to Logarithms (1 of 2: Definition)"},"longBylineText":{"runs":[{"text":"Eddie Woo","navigationEndpoint":{"clickTrackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@misterwootube","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCq0EGvLTyy-LLT1oUSO_0FQ","canonicalBaseUrl":"/@misterwootube"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"1,431,537 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"7 minutes, 53 seconds"}},"simpleText":"7:53"},"navigationEndpoint":{"clickTrackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=ntBWrcbAhaY","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"ntBWrcbAhaY","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=9ed056adc6c085a6 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1411250 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Eddie Woo","navigationEndpoint":{"clickTrackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@misterwootube","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCq0EGvLTyy-LLT1oUSO_0FQ","canonicalBaseUrl":"/@misterwootube"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kZuFfcyx3V7heWoK6stPlQpCsRAu0UnihqKT58AxBAuQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLchApouCttzVleieAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"1.4 million views"}},"simpleText":"1.4M views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKEBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKEBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"ntBWrcbAhaY","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKEBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["ntBWrcbAhaY"],"params":"CAQ%3D"}},"videoIds":["ntBWrcbAhaY"]}},{"clickTrackingParams":"CKEBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CKIBELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CKEBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtudEJXcmNiQWhhWQ%3D%3D","commands":[{"clickTrackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKABEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CJ0BEKQwGAMiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"7 minutes, 53 seconds"}},"simpleText":"7:53"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJ8BEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"ntBWrcbAhaY","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJ8BEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"ntBWrcbAhaY"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJ8BEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJ4BEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJ4BEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"ntBWrcbAhaY","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJ4BEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["ntBWrcbAhaY"],"params":"CAQ%3D"}},"videoIds":["ntBWrcbAhaY"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJ4BEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Introduction to Logarithms (1 of 2: Definition) - 7 minutes, 53 seconds - Go to channel - Eddie Woo - 1.4M views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/ntBWrcbAhaY/mqdefault_6s.webp?du=3000 sqp=CIDX5L0G rs=AOn4CLDnE7pwudWIDoMlkeFv-OxigPkxCw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"1Yv4fEsGpvM","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/1Yv4fEsGpvM/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCUqLOPHcV64G1QszzNJRHp6x1E9A","width":168,"height":94},{"url":"https://i.ytimg.com/vi/1Yv4fEsGpvM/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDapFVA2U8cmE5-dEFwoUk5gnADsQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions by Professor Dave Explains 104,388 views 7 years ago 8 minutes, 10 seconds"}},"simpleText":"Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions"},"longBylineText":{"runs":[{"text":"Professor Dave Explains","navigationEndpoint":{"clickTrackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@ProfessorDaveExplains","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC0cd_-e49hZpWLH3UIwoWRA","canonicalBaseUrl":"/@ProfessorDaveExplains"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"104,388 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"8 minutes, 10 seconds"}},"simpleText":"8:10"},"navigationEndpoint":{"clickTrackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=1Yv4fEsGpvM","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"1Yv4fEsGpvM","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nv47zne7.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=d58bf87c4b06a6f3 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=548750 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Professor Dave Explains","navigationEndpoint":{"clickTrackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@ProfessorDaveExplains","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC0cd_-e49hZpWLH3UIwoWRA","canonicalBaseUrl":"/@ProfessorDaveExplains"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lQiE1t-NjUuQDjIdIDpgyszdS3hI5TlIqZ1lr3PDewKDk=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLchA882a2MSP_sXVAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"104K views"}},"simpleText":"104K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJsBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJsBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"1Yv4fEsGpvM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJsBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["1Yv4fEsGpvM"],"params":"CAQ%3D"}},"videoIds":["1Yv4fEsGpvM"]}},{"clickTrackingParams":"CJsBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJwBELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CJsBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgsxWXY0ZkVzR3B2TQ%3D%3D","commands":[{"clickTrackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJoBEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CJcBEKQwGAQiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"8 minutes, 10 seconds"}},"simpleText":"8:10"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJkBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"1Yv4fEsGpvM","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJkBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"1Yv4fEsGpvM"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJkBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJgBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJgBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"1Yv4fEsGpvM","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJgBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["1Yv4fEsGpvM"],"params":"CAQ%3D"}},"videoIds":["1Yv4fEsGpvM"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJgBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Logarithms Part 1: Evaluation of Logs and Graphing Logarithmic Functions - 8 minutes, 10 seconds - Go to channel - Professor Dave Explains - 104K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/1Yv4fEsGpvM/mqdefault_6s.webp?du=3000 sqp=CLfP5L0G rs=AOn4CLAGjtzzrYIrwdf2w8ydw6SoQ1Qibw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"mQTWzLpCcW0","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/mQTWzLpCcW0/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBkxsEh71Is_SRczTJKW74hN2_Xug","width":168,"height":94},{"url":"https://i.ytimg.com/vi/mQTWzLpCcW0/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAkZCvfRXJp61kDskdYpkhv1fpTlA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Introduction to Logarithms by Khan Academy 2,301,589 views 17 years ago 9 minutes, 49 seconds"}},"simpleText":"Introduction to Logarithms"},"longBylineText":{"runs":[{"text":"Khan Academy","navigationEndpoint":{"clickTrackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@khanacademy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4a-Gbdw7vOaccHmFo40b9g","canonicalBaseUrl":"/@khanacademy"}}}]},"publishedTimeText":{"simpleText":"17 years ago"},"viewCountText":{"simpleText":"2,301,589 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 49 seconds"}},"simpleText":"9:49"},"navigationEndpoint":{"clickTrackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=mQTWzLpCcW0","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"mQTWzLpCcW0","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=9904d6ccba42716d ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1411250 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Khan Academy","navigationEndpoint":{"clickTrackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@khanacademy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC4a-Gbdw7vOaccHmFo40b9g","canonicalBaseUrl":"/@khanacademy"}}}]},"badges":[{"metadataBadgeRenderer":{"style":"BADGE_STYLE_TYPE_YPC","label":"Fundraiser","trackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcg="}}],"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_l3GggKOWViCBpDs9APIsK6MHB2Mu-ECo5dUEU-Vay2gg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLchA7eKJ0svZtYKZAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"2.3 million views"}},"simpleText":"2.3M views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJUBEP6YBBgIIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJUBEP6YBBgIIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"mQTWzLpCcW0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJUBEP6YBBgIIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["mQTWzLpCcW0"],"params":"CAQ%3D"}},"videoIds":["mQTWzLpCcW0"]}},{"clickTrackingParams":"CJUBEP6YBBgIIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJYBELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CJUBEP6YBBgIIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgttUVRXekxwQ2NXMA%3D%3D","commands":[{"clickTrackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJQBEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CJEBEKQwGAUiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 49 seconds"}},"simpleText":"9:49"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJMBEPnnAxgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"mQTWzLpCcW0","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJMBEPnnAxgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"mQTWzLpCcW0"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJMBEPnnAxgDIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CJIBEMfsBBgEIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJIBEMfsBBgEIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"mQTWzLpCcW0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJIBEMfsBBgEIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["mQTWzLpCcW0"],"params":"CAQ%3D"}},"videoIds":["mQTWzLpCcW0"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CJIBEMfsBBgEIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Introduction to Logarithms - 9 minutes, 49 seconds - Go to channel - Khan Academy - 2.3M views - 17 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/mQTWzLpCcW0/mqdefault_6s.webp?du=3000 sqp=CPXD5L0G rs=AOn4CLDqkpGprM-bZSccq-xO2KDXlVpjAw","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"mc8Ki0_yzWA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/mc8Ki0_yzWA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLAEI4_OIPEoZrjkiffkYg3BIDbEUw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/mc8Ki0_yzWA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLB0hV6s8yMYfH_tBbwSW_nYPhwjdQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases) by Math and Science 408,473 views 4 years ago 45 minutes"}},"simpleText":"15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)"},"longBylineText":{"runs":[{"text":"Math and Science","navigationEndpoint":{"clickTrackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathAndScience","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCYgL81lc7DOLNhnel1_J6Vg","canonicalBaseUrl":"/@MathAndScience"}}}]},"publishedTimeText":{"simpleText":"4 years ago"},"viewCountText":{"simpleText":"408,473 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"45 minutes"}},"simpleText":"45:00"},"navigationEndpoint":{"clickTrackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=mc8Ki0_yzWA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"mc8Ki0_yzWA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=99cf0a8b4ff2cd60 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=2268750 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Math and Science","navigationEndpoint":{"clickTrackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathAndScience","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCYgL81lc7DOLNhnel1_J6Vg","canonicalBaseUrl":"/@MathAndScience"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/KG4-MPi-rWInkcl04h8xsCql5DnPXjn8RGKVXJmu1ULPQY4vKIDv7jvlbRYmOoLNvVFKQl1pMQ=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLchA4JrL_7TRwueZAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"408K views"}},"simpleText":"408K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CI8BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CI8BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"mc8Ki0_yzWA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CI8BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["mc8Ki0_yzWA"],"params":"CAQ%3D"}},"videoIds":["mc8Ki0_yzWA"]}},{"clickTrackingParams":"CI8BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CJABELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CI8BEP6YBBgGIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgttYzhLaTBfeXpXQQ%3D%3D","commands":[{"clickTrackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CI4BEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CIsBEKQwGAYiEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"45 minutes"}},"simpleText":"45:00"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CI0BEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"mc8Ki0_yzWA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CI0BEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"mc8Ki0_yzWA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CI0BEPnnAxgBIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CIwBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CIwBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"mc8Ki0_yzWA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CIwBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["mc8Ki0_yzWA"],"params":"CAQ%3D"}},"videoIds":["mc8Ki0_yzWA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CIwBEMfsBBgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases) - 45 minutes - Go to channel - Math and Science - 408K views - 4 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/mc8Ki0_yzWA/mqdefault_6s.webp?du=3000 sqp=CMDJ5L0G rs=AOn4CLBP9PnzQSkUj1UFFpeb58grm21Mtg","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"C9MiG9OrktA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/C9MiG9OrktA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCFNm8cbtYTFxp8_zlCpvLAimN-VA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/C9MiG9OrktA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDEIKNUZ6tzztTNEnbKVEiNON93gw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"گوشی ایرانی خریدم! بزرگ ترین اشتباه زندگیم🤦😂 by Milad1st 343,701 views 2 days ago 25 minutes"}},"simpleText":"گوشی ایرانی خریدم! بزرگ ترین اشتباه زندگیم🤦😂"},"longBylineText":{"runs":[{"text":"Milad1st","navigationEndpoint":{"clickTrackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Milad1st1","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCRIZRnaadnc_NuZWGI27d0w","canonicalBaseUrl":"/@Milad1st1"}}}]},"publishedTimeText":{"simpleText":"2 days ago"},"viewCountText":{"simpleText":"343,701 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"25 minutes, 41 seconds"}},"simpleText":"25:41"},"navigationEndpoint":{"clickTrackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWRI5daKtcLFgPoSmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=C9MiG9OrktA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"C9MiG9OrktA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=0bd3221bd3ab92d0 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1411250 mt=1740189904 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Milad1st","navigationEndpoint":{"clickTrackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcgyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Milad1st1","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCRIZRnaadnc_NuZWGI27d0w","canonicalBaseUrl":"/@Milad1st1"}}}]},"badges":[{"metadataBadgeRenderer":{"style":"BADGE_STYLE_TYPE_SIMPLE","label":"New","trackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcg="}}],"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/yjpU7cJQ_yu2UdZRK3ZQXI_xfdrbU1jyXTQqi9aRT8mS0adgD9GY_mzGbCjZy1IYuZMRz8igYg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLchA0KWunb3DyOkL","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"343K views"}},"simpleText":"343K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CIkBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CIkBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"C9MiG9OrktA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CIkBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["C9MiG9OrktA"],"params":"CAQ%3D"}},"videoIds":["C9MiG9OrktA"]}},{"clickTrackingParams":"CIkBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CIoBELlqIhMIrKKylJrWiwMVTkJ6BR390S3I"}},"popupType":"TOAST"}}]}},"trackingParams":"CIkBEP6YBBgHIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtDOU1pRzlPcmt0QQ%3D%3D","commands":[{"clickTrackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CIgBEI5iIhMIrKKylJrWiwMVTkJ6BR390S3I","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcg=","hasSeparator":true}}],"trackingParams":"CIUBEKQwGAciEwisorKUmtaLAxVOQnoFHf3RLcg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"25 minutes, 41 seconds"}},"simpleText":"25:41"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CIcBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"C9MiG9OrktA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CIcBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"C9MiG9OrktA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CIcBEPnnAxgCIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CIYBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CIYBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"C9MiG9OrktA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CIYBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["C9MiG9OrktA"],"params":"CAQ%3D"}},"videoIds":["C9MiG9OrktA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CIYBEMfsBBgDIhMIrKKylJrWiwMVTkJ6BR390S3I"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"گوشی ایرانی خریدم! بزرگ ترین اشتباه زندگیم🤦😂 - 25 minutes - Go to channel - Milad1st - 343K views - 2 days ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/C9MiG9OrktA/mqdefault_6s.webp?du=3000 sqp=CODI5L0G rs=AOn4CLDBwPo72VWlnsngqFlmAcnTOmkENg","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/EvQCLCaiq2U/hqdefault.jpg?sqp=-oaymwEwCKgBEF5IWvKriqkDIwgBFQAAiEIYAfABAfgB_gSAAuADigIMCAAQARhlIFcoUjAP rs=AOn4CLD_B8bIawZrOEalUGI0hhW7u0taMg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/EvQCLCaiq2U/hqdefault.jpg?sqp=-oaymwExCNACELwBSFryq4qpAyMIARUAAIhCGAHwAQH4Af4EgALgA4oCDAgAEAEYZSBXKFIwDw== rs=AOn4CLBpqCCPCVztii0AMksb1n29_cN9HA","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"COURSE"}}]},"text":"16 lessons","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3353385,"darkTheme":3353385}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4142643,"darkTheme":4142643}}},"stackColor":{"lightTheme":10060668,"darkTheme":9666423}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Thinkwell's College Algebra: 6.2 Logarithmic Functions"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"ThinkwellVids

#############################