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

1. Jul 16, 2009

### 3hlang

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

2. Jul 16, 2009

### tiny-tim

Hi 3hlang!
Nope!

3. Jul 16, 2009

### HallsofIvy

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).

4. Jul 16, 2009

### g_edgar

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

5. Jul 22, 2009

### 3hlang

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

6. Jul 22, 2009

### 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)).

7. Jul 22, 2009

### 3hlang

what? i wasn't claiming to have done anything radical to the formula. all i wanted to know was what you do the w function of. but thank you for telling me