Answer
$2$
Work Step by Step
Recall:
$\log_a{\left(a^n\right)}=n$
Using the rule above, and knowing the the natural logarithms has base $e$, gives:
\begin{align*}
\ln{\left(e^2\right)}&=\log_e{\left(e^2\right)}\\
&=2
\end{align*}