Answer
See explanations.
Work Step by Step
Step 1. Let $p=log_ax$, we have $x=a^p$
Step 2. We have $x^r=(a^p)^r=a^{pr}$, thus $pr=log_a(x^r)$
Step 3. Combine the above, we have $(log_ax)r=log_a(x^r)$ or $log_a(x^r)=r\ log_ax$
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