# How to solve for x in 36=X^X?

1. Jan 25, 2012

I came up with an idea for an equation, which follows: 36=X^X. I tried solving it, but I couldn't. I found the graphically (3.15, if I recall correctly), but I want to know if there's a way to solve it algebraically.

2. Jan 25, 2012

### tiny-tim

nope!

3. Jan 25, 2012

### Char. Limit

Actually, you can, but you need to use the Lambert-W Function.

4. Jan 26, 2012

### RamaWolf

Let f(x):=x$^{x}$ - 36, (f(x) is continuous, f(3.1) < 0, f(3.2) > 0) we can apply

the 'half intervall' function I implemented in my ARIBAS_W workbench, to find the zero of f(x)

in the intervall (3.1,3.2) as: 3.13564239388907368