Answer
Since $\log_a {x}+\log_a {y}=log_a {x\cdot y}$, then
$f(AB)=\log_a{AB}=\log_a{A}+\log_a{B}=f(A)+f(B)$
Work Step by Step
We know that $\log_a {x}+\log_a {y}=log_a {x\cdot y}$.
Hence,
$f(AB)\\
=\log_a{AB}
\\=\log_a{A}+\log_a{B}
\\=f(A)+f(B)$
