rational ^ sqrt(5) = rational ?

[Gerenuk]

I've programmed an algorithm to numerically compute the logarithm of numbers in phinary base easily. I could avoid float multiplications if I can find a pair of rational numbers x and y such that
x^{\sqrt{5}}=y
Is it possible?
Probably not, but I cannot prove it :(

[gel]

No, it isn't possible except for the obvious x=y=1. There's a theorem (http://en.wikipedia.org/wiki/Gelfond–Schneider_theorem) which says that it's impossible.