Uploaded February 2024 | Updated September 2026, 2 weeks ago
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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: youtube.com/playlist?list=PLj7p5OoL6vGxHsQjgCw5Nfe8O3o8fu3LV
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
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π Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
πͺ Get my math notes by becoming a patron: patreon.com/blackpenredpen
#blackpenredpen #math #calculus #apcalculus
Get started with a 30-day free trial on Brilliant: πbrilliant.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: youtube.com/playlist?list=PLj7p5OoL6vGxHsQjgCw5Nfe8O3o8fu3LV
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
----------------------------------------
π Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
πͺ Get my math notes by becoming a patron: patreon.com/blackpenredpen
#blackpenredpen #math #calculus #apcalculus
