Q:

Taking natural log of $f(x) = 5^{x^2}$

$$f(x) = 5^{x^2}$$
I'm trying to figure out how to take the natural log of this problem. All rules that I can find for natural log don't explain what to do with multiple exponents. Can someone please explain how to do this? Thanks.

A:

You use the rule $\log(a^b) = b\log(a)$ as follows:
$$\log\left(5^{x^2}\right) = x^2\log(5).$$
Here $b=x^2$, and $a=5$.

