Answer
$x=6$
Work Step by Step
Let $2^{\log_2 6}=x$. Taking the logarithm base $2$ of both sides, then,
\begin{array}{l}
\log_2 2^{\log_2 6}=\log_2x
\\
(\log_2 6)(\log_2 2)=\log_2x
\\
(\log_2 6)(1)=\log_2x
\\
\log_2 6=\log_2x
.\end{array}
Since the bases on both sides of the equal sign are the same, then the logarithm base $2$ can be dropped, resulting to $
x=6
.$
