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?