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


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