## Natural logarithm and pi... help?

I haven't been able to prove:

ln(e)/e > ln(pi)/pi

without calculating any of the values. Help would be much appreciated.

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 Recognitions: Gold Member Homework Help Science Advisor Hint: Consider the function $$f(x)=\frac{ln(x)}{x}}$$, with domain the positive real half-axis. Determine the function's maximum value.
 mm, I can see that, but I was looking for a proof that shows that e^pi > pi^e

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Homework Help
$$\pi(ln(e))>eln(\pi)\to{ln}(e^{\pi})>ln(\pi^{e})$$