The problem asks to evaluate the expression $\log_m{m^{2n}}$.

1. Problem Description

The problem asks to evaluate the expression $\log_m{m^{2n}}$.

2. Solution Steps

We can use the property of logarithms that states $\log_a{a^x} = x$. In this case, we have $a = m$ and $x = 2n$. Therefore,

$\log_m{m^{2n}} = 2n$.

3. Final Answer

2n