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Which is greater e^pi or pi^e?

Poly

Member
Nov 26, 2012
32
Which is greater, $e^{\pi}$ or $\pi^{e}$?

I found this when searching for calculus inequalities.
 
Last edited by a moderator:

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
A variation of the same method is to raise both numbers to power $1/(e\pi)$ and find the maximum of $x^{1/x}$.