College Algebra, Chapter 5, 5.3, Section 5.3, Problem 30

Expand the expression $\displaystyle \log_a \left( \frac{x^2}{yz^3} \right)$, using Laws of Logarithm


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\begin{equation}
\begin{aligned}

\log_a \left( \frac{x^2}{yz^3} \right) =& \log_a (x^2) - \log_a (yz^3)
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
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\log_a \left( \frac{x^2}{yz^3} \right) =& \log_a (x^2) - \left( \log_a y + \log_a (z^3) \right)
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
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\log_a \left( \frac{x^2}{yz^3} \right) =& 2 \log_a x - (\log_a y + 3 \log_a z)
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
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\log_a \left( \frac{x^2}{yz^3} \right) =& 2 \log_a x - \log_a y - 3 \log_a z
&& \text{Distributive Property}


\end{aligned}
\end{equation}
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