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How can I calculate without calculator or something like this

the values of $\gamma^e$ and $e^\gamma$

in order to compare them?

($\gamma$ the Euler-Mascheroni constant)

Note: the shape of this question lend from the beautiful question of Mirzodaler >>> here.

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al-Hwarizmi
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    Have you read the solutions on the page you mention? Because if you did, you should realize that the solution is already mentioned. – Raskolnikov Jun 16 '13 at 09:45
  • The Mascheroni constant? may you help how and where? – al-Hwarizmi Jun 16 '13 at 09:47
  • Some of the tricks mentioned don't depend on it being the Mascheroni constant or the Avogadro number or whatever. – Raskolnikov Jun 16 '13 at 09:49
  • Got it! Robin Chapman! I think we wrote in parallel perhaps. – al-Hwarizmi Jun 16 '13 at 09:51
  • The question about $\pi$ is not immediate because both $e$ and $\pi$ are relatively close to $3$. Here, since $\gamma\approx 0.5$ it is obvious that one is larger than $1$ whereas the other is clearly not. – L. F. Jun 16 '13 at 10:21

1 Answers1

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Since $$γ^e=e^{e\lnγ}$$ So,the problem is comparing $γ$ and $e\lnγ$, as well as,the sign of $γ-e\lnγ$. Consider the function $$f(x)=x-e\ln x$$ and its monotony.

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