Answer
False;
Correct Statement:
$\ln{e^e} = e$
Work Step by Step
RECALL:
$\ln_b{x}=y \longrightarrow e^y=x$
Thus, if
$\ln{0}=y$, then $e^y=0$
However, $e^0=1$, not $0$.
Therefore, the statement is false.
A correct statement would be: $\ln{e^e} =e$.