College Algebra, Chapter 5, 5.3, Section 5.3, Problem 52

Combine the expression $\displaystyle 2 (\log_5 x + 2 \log_5 y - 3 \log_5 z)$, using the Laws of Logarithm


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\begin{equation}
\begin{aligned}

2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& 2 \left( \log_5 x + \log_5 y^2 - \log_5 z^3 \right)
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
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2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& 2 \left( \log_5 xy^2 - \log_5 z^3 \right)
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
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\\
2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& 2 \log_5 \left( \frac{xy^2}{z^3} \right)
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
2 (\log_5 x + 2 \log_5 y - 3 \log_5 z) =& \log_5 \left( \frac{xy^2}{z^3} \right)^2
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A

\end{aligned}
\end{equation}
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