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

(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).