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e and pi (Posted on 2003-09-26) Difficulty: 4 of 5
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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re: Solution | Comment 3 of 7 |
(In reply to Solution by SilverKnight)

By the way:

I wrote, in my solution, that:
"...the question is equivalent to taking the natural log (ln) of both sides and determining the inequality relationship there."

This is true, because if I have two functions F and G which have an inequality relationship (such as F < G ), I can perform an operation (such as taking the natural log of both) that keeps the sign (positive) and is monotonically increasing (to maintain the inequality).
  Posted by SilverKnight on 2003-09-26 14:32:23

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