Let $\log_a$ be the D866: Standard real logarithm function in base $a \in (0, \infty) \setminus \{ 1 \}$.
Let $x, y \in (0, \infty)$ each be a D5407: Positive real number.
Let $x, y \in (0, \infty)$ each be a D5407: Positive real number.
Then
\begin{equation}
\log_a (x y)
= \log_a x + \log_a y
\end{equation}