College Algebra, Chapter 5, Review Exercise, Section Review Exercise, Problem 48

Expand the Logarithmic Expression $\displaystyle \log \left( \frac{4x^3}{y^2 (x - 1)^5} \right)$

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\begin{equation}
\begin{aligned}
\log \left( \frac{4x^3}{y^2 (x - 1)^5} \right) &= \log 4x^3 - \log y^2 (x - 1)^5 && \text{Laws of Logarithm } \log_a \frac{A}{B} = \log_a A - \log_a B\\
\\
\log \left( \frac{4x^3}{y^2 (x - 1)^5} \right) &= \log 4 + \log x^3 - \left( \log y^2 + \log (x - 1)^5 \right) && \text{Laws of Logarithm } \log_a AB = \log_a A + \log_a B\\
\\
\log \left( \frac{4x^3}{y^2 (x - 1)^5} \right) &= \log 4 + 3 \log x - ( 2 \log y + 5 \log (x - 1)) && \text{Laws of Logarithm } \log_a A^c = C\log_a A\\
\\
\log \left( \frac{4x^3}{y^2 (x - 1)^5} \right) &= \log 4 + 3 \log x - 2 \log y - 5 \log (x - 1) && \text{Distributive Property}
\end{aligned}
\end{equation}
$