College Algebra, Chapter 5, 5.3, Section 5.3, Problem 46

Combine the expression $\displaystyle \log 12 + \frac{1}{2} \log 7 - \log 2$, using the Laws of Logarithm


$\begin{equation} \begin{aligned} \log 12 + \frac{1}{2} \log 7 - \log 2 =& \log 12 + \log 7^{\frac{1}{2}} - \log 2 && \text{Law of Logarithm } \log_a (A^C) = C \log_a A \\ \\ \log 12 + \frac{1}{2} \log 7 - \log 2 =& \log \left( 12 \sqrt{7} \right) - \log 2 && \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B \\ \\ \log 12 + \frac{1}{2} \log 7 - \log 2 =& \log \left( \frac{12 \sqrt{7}}{2} \right) && \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B \\ \\ \log 12 + \frac{1}{2} \log 7 - \log 2 =& \log \left( 6 \sqrt{7} \right) && \text{Reduce to lowest term} \end{aligned} \end{equation}$