Using result
R3498: Homomorphism property of the standard natural logarithm, we have
\begin{equation}
\log_a \left( \prod_{n = 1}^N x_n \right)
= \frac{\log \left( \prod_{n = 1}^N x_n \right)}{\log a}
= \frac{\sum_{n = 1}^N \log x_n}{\log a}
= \sum_{n = 1}^N \frac{\log x_n}{\log a}
= \sum_{n = 1}^N \log_a x_n
\end{equation}
$\square$
