#### Answer

False, $log_{b}x^{r}=rlog_{b}x$

#### Work Step by Step

We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number).
Therefore, the given statement is false.
$log_{b}x^{r}\ne log_{b}rx$
Instead, $log_{b}x^{r}=rlog_{b}x$.