Find an upper bound for $ x$

Question

If $f_1(x)=x, f_2(x)=x^x, f_{n+1}(x)=x^{f_n(x)}$ for $x \geq 1$ and $n \geq 1$.

How do you find an upper bound for $x$ as $n \to \infty$ where f_n(x) exists.