Answer
Since $\log_a {x^n}=n\cdot \log_a {x}$, then
$f(x^{\alpha})=\log_a{(x^{\alpha})}=\alpha \cdot \log_a{x}=\alpha \cdot f(x)$
Work Step by Step
We know that $\log_a {x^n}=n\cdot \log_a {x}$.
Hence,
$f(x^{\alpha})=\log_a{x^{\alpha}}=\alpha \cdot \log_a{x}=\alpha \cdot f(x)$
