How to differentiate $\ln(a^x)$?

Question

Can someone give me the process to differentiate this (with respect to $x$)?

$$ \ln(a^x) $$

Answer 1

Since $$\ln(a^x) = x\ln a,$$ you can see that this function is in fact linear in $x$. (Note that $\ln a$ is just some constant.) The derivative is therefore $1 \cdot \ln a= \ln a.$

Answer 2

Hint:

Use the fact that $$a^x = e^{x\ln a}.$$