Is this equation solvable xln4xln10xln25
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Get started with a 30-day free trial on Brilliant: 👉https://brilliant.org/blackpenredpen/ ( 20% off with this link!) • We will solve this power equation x^ln(4)+x^ln(10)=x^ln(25). However, the process of solving this equation would require making one side equal to 0 but factoring every term by x^ln(4), and I don't think the expressions will look that nice. So instead, we can use the log property that a^logb(c)=c^logb(a) and change the equation to an exponential equation. The answer will involve the usage of the quadratic formula and we will also see the golden ratio. • Equation-of-the-year playlist: • Equation Of The Year! • 0:00 Math for fun, solving the power equation x^ln(4)+x^ln(10)=x^ln(25) • 1:09 Proving a^logb(c)=c^logb(a) • 3:18 Solving the equation in exponential form • 8:35 Check out Brilliant • ---------------------------------------- • 🛍 Shop my math t-shirt hoodies: https://amzn.to/3qBeuw6 • 💪 Get my math notes by becoming a patron: / blackpenredpen • #blackpenredpen #math #calculus #apcalculus
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