Intermediate Algebra (6th Edition)

$x=6$
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 $x=6 .$