perplexus.info :: Just Math : e and pi

e and pi (Posted on 2003-09-26)

Without finding the numerical values, show which is greater, e^π or π^e.

See The Solution Submitted by DJ

Rating: 4.1429 (14 votes)

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Comment on official solution

| Comment 5 of 7 |

From the official solution...

"The underlying idea here is that a^b > b^a whenever b > a, given that a and b are both greater than 1."

This is incorrect. A counterexample is a = 2, b = 3.

Edited on June 13, 2004, 2:07 pm

Posted by Nick Hobson on 2004-06-13 14:05:45

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