is it $e^\pi<\pi^e$ or $\pi^e<e^\pi$? it's an interesting question that just came to my mind, well of course I used the calculator to get the answer, However I need to like prove it and I don't know where I should start from.
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Hint: show that $f(x) = \ln(x)/x$ is decreasing on $x>e$. – Brian Moehring Feb 18 '22 at 23:31
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2$\pi^e<e^{\pi}$, and this has definitely been asked before. – peek-a-boo Feb 18 '22 at 23:32
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the relationship is not specific to $\pi$, see the following question: Why $e^x$ is always greater than $x^e$?
Samual
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