Which is greater e^pi or pi^e?

Poly

Member
Which is greater, $e^{\pi}$ or $\pi^{e}$?

I found this when searching for calculus inequalities.

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MHB Math Helper

Evgeny.Makarov

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