Answer
$0$
Work Step by Step
Start with the innermost argument, $\ln e$. Since $\ln e^a=a$ and $e=e^1$, $\ln e=\ln e^1=1$. Therefore, $\ln(\ln e)=\ln(1)$ since $1=e^{0}$, $$\ln(\ln e)=\ln(e^0)=0$$
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