# How to prove that $e^\pi>\pi^e$ [duplicate]

How can one prove that $e^\pi>\pi^e$ ? Should I use logarithms or something like that? Or is there a gentle smart way of proving so?

## marked as duplicate by Sujaan Kunalan, MJD, MCT, Blue, achille huiApr 17 '14 at 18:30

$e^n>1+n$ given $n>0$. Now see what happens when $n=\dfrac \pi e-1$.
• $n$ seems an un-natural choice of variable, no? (+1 though) – anaconda Apr 17 '14 at 18:08