(In reply to

Not sure if rigorous but... by Kenny M)

You say:

"*take the 0.4th root of both sides:*

*x^0.4^(x/0.4) = 0.4^x"*

But:

*The given equation is X^(0.4^X) = 0.4^(X^0.4)*

Taking the 0.4th root on both sides, we have:

X^((0.4^X)/0.4) = 0.4^((X^0.4)/0.4)

Or, X^((0.4^(X-1)) = 0.4^((X^0.4)/0.4)

*** Your error lies in assuming that X^(0.4^X) = (X^0.4)^X, which is not true since:

(X^0.4)^X = X^(0.4*X), and we cannot have:

X^(0.4^X) = X^(0.4*X)

*** The value of a^(b^c) as defined in the problem is similar to the wikipedia article on integer exponentiation in the following location.

http://en.wikipedia.org/wiki/Exponentiation#Identities_and_properties

Regards,

K Sengupta

*Edited on ***March 11, 2008, 2:58 am**