Answer
$0.874$
Work Step by Step
Change of Base Formula: $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$
$\log_{\pi} e= \dfrac{\log_{10} e}{\log_{10} \pi}$
Where: $a=\pi \hspace{10pt} M = e \hspace{10pt} b = 10$
$ \dfrac{\log_{10} e}{\log_{10} \pi} \approx \boxed{0.874}$