College Algebra, Chapter 5, 5.3, Section 5.3, Problem 54

Combine the expression $\displaystyle \log_a b + c \log_a d - r \log_a s$, using the Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\log_a b + c \log_a d - r \log_a s =& \log_a b + \log_a d^c - \log_a s^r
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
\\
\\
\log_a b + c \log_a d - r \log_a s =& \log_a bd^c - \log_a s^r
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
\\
\\
\log_a b + c \log_a d - r \log_a s =& \log_a \frac{bd^c}{s^r}
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B

\end{aligned}
\end{equation}
$