If $2^n=3^m$ and both $n,m$ are integers, which one is greater?

Question

If $n$ and $m$ are whole numbers. $$2^n = 3^m$$ Which one is bigger, $n$ or $m$?

I don't know how to approach this question.

Answer 1

$3^m$ is never an even number. Since $2^n=3^m$, that means that $2^n$ is not even. The only way for that to happen would be for $n=0$ and $2^n=1$. Since $2^n=3^m$, we have that $3^m=1$ and $m=0$. This:

The only solution is $n=0$ and $m=0$. Also, neither is bigger.

This all assumes that $n$ and $m$ are whole numbers. Without that, this all goes out the window.