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

kspcr111 | Student

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 `