I found the x^(x^3)=3 solution in the site quite interesting and was thinking: what about x^x=a? I have tried hard to solve the problem but i couldnt do it. And what of f(x)=a where f(x)=x^(x^(x^(x^x)))=a and there are n recurrent cases, similar to the one in the x^(x^3) page?

>I have tried hard to
>solve the problem but i couldnt do it.

You probably tried to express the solution by means of the so-called elementary function, right? sin(x), cos(x), xn, ax, etc... This is impossible.

The solution to xx = a is given by the Lambert function invent specifically for that purpose. See, for example,

http://mathworld.wolfram.com/LambertsW-Function.html