`4^x = 5^(x^2)` Solve the exponential equation algebraically. Approximate the result to three decimal places.

Textbook Question

Chapter 3, 3.4 - Problem 37 - Precalculus (3rd Edition, Ron Larson).
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kspcr111 | In Training Educator

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Given

`4^x = 5^(x^2)`

applying logarithims on both sides

we get

`ln(4^x) = ln(5^(x^2))`

=> `xln(4) = x^2 (ln(5))`

=> `ln(4) = x (ln(5))`

`x = ln(4) / ln(5) = 0.8613` or `x= 0 `

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