f(x) greater than g(x) when x > 2 explanation

Question

Where $f(x) = (x^x)^x$ and $g(x) = x^{(x^x)}$. How do I go about showing that one of these functions is always greater than the other for all $x > 2$?

Could I use induction? I've gone through it with induction a bit but it doesn't seem very useful...

Thanks in advance!

Answer 1

If $x>2, x^x>x^2$ and then $g(x)>f(x)$.

Induction is only for integers.