Answer
The statement, $\log {{x}^{a}}=x\ln a$ is false.
Work Step by Step
$\log {{x}^{a}}=x\ln a$
The base of the common logarithm is 10, and the base of the natural logarithm is e, so they both are not equal.
The power rule for logarithms says that, for any positive numbers M, N and a $\left( a\ne 1 \right)$, ${{\log }_{a}}{{M}^{p}}=p\cdot {{\log }_{a}}M$.
Therefore, $\log {{x}^{a}}=a\log x$.
So, both the ways in the given statement are wrong.
