# Natural logarithm and pi... help?

by Guero
Tags: logarithm, natural
 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.
 Sci Advisor 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: $$\pi(ln(e))>eln(\pi)\to{ln}(e^{\pi})>ln(\pi^{e})$$ wherefrom your inequality follows.