Exponential and Logarithmic Functions · Challenge problem

Solve the base-tower equation $\displaystyle 2^{\,2^{x}}-5\cdot 2^{\,2^{\,x-1}}+4=0$. (Hint: let $y=2^{\,2^{x-1}}$ and note $2^{\,2^{x}}=y^{2}$.)