# If y=x^x then what is x in terms of y?

i know this is possible to find with iteration, but is it possible to find it algebraically?

tiny-tim
Homework Helper
Hi 3hlang!
i know this is possible to find with iteration, but is it possible to find it algebraically?

Nope!

HallsofIvy
Homework Helper
This probably isn't what you mean by "algebraically" but if you take the logarithm of both sides of the equation you get ln(y)= xln(x) and then x= W(ln(y)) where W is the "Lambert W function" which is defined as the inverse function to xln(x).

... and the reason we talk about the Lambert W function is that none of the previously-defined standard functions would work.

so if x=y^y, then y=?

HallsofIvy
All you have done is swap x and y! If $x= y^y$ then, by the same formula I gave before, y= W(ln(x)).