Properties of Logarithms to simplify $\log\left(3^{(5^7)}\right)$

Question

How do you simplify the following expression? $$\log\left(3^{(5^7)}\right)$$ I know that logarithms are like the inverse of exponents, but are there any tricks to simplify powers inside logarithms?

Edit: There are five answer choices:

(A) $7\log(3^5)$

(B) $35\log(3)$

(C) $7(\log(3))(\log(5))$

(D) $7(\log(3)+\log(5))$

(E) $5^7\log(3)$

Answer 1

As $\displaystyle \log(a^m)=m\log a$ where both $\log$ remain defined

Here $a=3, m=5^7$

Answer 2

$\log 3^{(5^7)}=5^7\log 3$

The power on the inside become multiplication on the outside, and becomes the simplest form (unless you want to turn $5^7$ into a single long number instead of that power)