College Algebra, Chapter 5, 5.3, Section 5.3, Problem 12

Evaluate the expression $\displaystyle \log_{12} 9 + \log_{12} 16$


$\begin{equation} \begin{aligned} \log_{12} 9 + \log_{12} 16 =& \log_{12} (9 \cdot 16) && \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B \\ \\ \log_{12} 9 + \log_{12} 16 =& \log_{12} (144) && \text{Simplify} \\ \\ \log_{12} 9 + \log_{12} 16 =& 2 && \text{Because } 12^2 = 144 \end{aligned} \end{equation}$