Answer
False.
To become true, change it to
$\log_{2}x^{4}=4\log_{2}x $
Work Step by Step
Applying the Power Rule to the RHS, $\log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$4\log_{2}x=\log_{2}x^{4}\quad\neq(\log_{2}x)^{2}$
so the statement is false.
