# Natural logarithm and pi... help?

by Guero
Tags: logarithm, natural
 P: 15 I haven't been able to prove: ln(e)/e > ln(pi)/pi without calculating any of the values. Help would be much appreciated.
 Sci Advisor HW Helper PF Gold P: 12,016 Hint: Consider the function $$f(x)=\frac{ln(x)}{x}}$$, with domain the positive real half-axis. Determine the function's maximum value.
 P: 15 mm, I can see that, but I was looking for a proof that shows that e^pi > pi^e
HW Helper
PF Gold
P: 12,016

## Natural logarithm and pi... help?

Well, since you can prove that ln(e)/e is the maximum value for f, we also have:
$$\pi(ln(e))>eln(\pi)\to{ln}(e^{\pi})>ln(\pi^{e})$$