Time to sketch a graph

• The equation in general has two solutions given by $\displaystyle x=e^{-W(\frac{-\ln 2}{2})}$ which gives $x=2,4$

W(.) - Lambert W function

So we don't worry so much about x>2 to start with so then what we do is

$2^x=x^2$

so

$x=\sqrt{2^x}$

so

$x=\sqrt{2^{\sqrt{2^{\sqrt{2^x}}}}}$

and we find solutions to this and one of them is $4$

and $4>2$

and $4^2=16$

so the answer is 16