Answer
$x=\frac{\ln{10}}{\ln{2}}\approx3.322$
Work Step by Step
Take the $\log_2$ of both sides:
$\log_2{(2^x)}=\log_2{10}\\
x=\log_2{10}$
We know that $\log_a{b}=\frac{\log_c{b}}{\log_c{a}}$.
Hence,
$x=\log_2{10}=\frac{\ln{10}}{\ln{2}}\approx3.322.$
