Problem (Algebra):
What is the value of $x$ such that $\log _{2}\left(\log _{2}(2 x-2)\right)=2$ ?

Solution:
$$
\begin{aligned}
\log _{2}\left(\log _{2}(2 x-2)\right) & =2 \\
\log _{2}(2 x-2) & =2^{2} \\
2 x-2 & =2^{\left(2^{2}\right)} \\
2 x-2 & =2^{4} \\
2 x-2 & =16 \\
2 x & =18 \\
x & =9
\end{aligned}
$$

Final answer: 9