Home > Inequality > Prove that e^pi > pi^e , Inequality

Prove that e^pi > pi^e , Inequality

e^{\pi} > {\pi}^e

You can use natural logarithm to prove this equality. You will get

\pi > e \cdot \ln \pi

\pi/e > \ln \pi

Let the f(x)=x/e & g(x)=lnx . f(x) is a line and g(x) is a hyperbole. The graphs of this functions touch each other at point x=e and f(x) always bigger than g(x) except point x=e.

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Categories: Inequality Tags: , , ,
  1. November 25, 2011 at 14:03

    You should use

     \ln 

    instead of

     ln 

    to parse \ln .

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