College Algebra, Chapter 5, 5.3, Section 5.3, Problem 34

Expand the expression $\displaystyle \log \left( \frac{a^2}{b^4 \sqrt{c}} \right)$, using Laws of Logarithm


$\begin{equation} \begin{aligned} \log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& \log a^2 - \log (b^4 \sqrt{c}) && \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B \\ \\ \log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& \log a^2 - (\log b^4 + \log \sqrt{c}) && \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B \\ \\ \log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& 2 \log a - \left( 4 \log b + \frac{1}{2} \log C \right) && \text{Law of Logarithm } \log_a (A^C) = C \log_a A \\ \\ \log \left( \frac{a^2}{b^4 \sqrt{c}} \right) =& 2 \log a - 4 \log b - \frac{1}{2} \log c && \text{Distributive Property} \end{aligned} \end{equation}$