logarithm inequality proof

Question

I'm trying to prove the following

Log($A^m$)> Log$(\frac{B^m}{A^m})$

Where $A \in \mathbb{R}$ and $B \in \mathbb{R}$. $m \in [1,\infty]$.

Any hints will be appreciated

Answer 1

We need to prove that: $$A^{2m}>B^m.$$ I think, now easy to find a counterexample.

I found $A=1$ and $B=2$.