log laws and derivatives of exponentials

Question

I am trying to determine the derivative of 4(7^x). I know the answer is 4(7^x)ln(7), but why can’t the answer be simplified to (7^x)ln(7^4) = (7^x)ln(2401) ?

Answer 1

They are equivalent.

Ultimately, your quesiton boils down to which is simpler $(4\ln 7)$ or $\ln 7^4 = \ln 2401$.

That is if $a\ln b$ is simpler or is $\ln b^a$ is simpler.