Answer
$$\text{False}$$
Work Step by Step
This is a wrong interpretation of the logarithm power rule
$\log M^{n}=n\log M$
For a counterexample, using the fact that $\ln e^{n}=n$, take $x=e^{9}:$
$LHS=(\ln e^{9})^{1/2}=(9)^{1/2}=3$
$RHS=\displaystyle \frac{1}{2}\ln e^{9}=\frac{1}{2}\cdot 9=4.5$
$(LHS\neq RHS)$
