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


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\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
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\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
\\
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\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
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\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}
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