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.

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

You should use

 \ln

 ln

to parse $\ln$ .