College Algebra, Chapter 5, Review Exercise, Section Review Exercise, Problem 50

Expand the Logarithmic Expression $\displaystyle \ln \left( \frac{3\sqrt{x^4 + 12}}{(x + 16) \sqrt{x-3}} \right)$

$
\begin{equation}
\begin{aligned}
\ln \left( \frac{3\sqrt{x^4 + 12}}{(x + 16) \sqrt{x-3}} \right) &= \ln \sqrt[3]{x^4 + 12} - \ln (x + 16) \sqrt{x-3} && \text{Laws of Logarithm } \log_a \frac{A}{B} = \log_a A - \log_a B\\
\\
\ln \left( \frac{3\sqrt{x^4 + 12}}{(x + 16) \sqrt{x-3}} \right) &= \ln \sqrt[3]{x^4 + 12} - [\ln (x + 16) + \ln \sqrt{x-3}]&& \text{Laws of Logarithm } \log_a AB = \log_a A + \log_a B\\
\\
\ln \left( \frac{3\sqrt{x^4 + 12}}{(x + 16) \sqrt{x-3}} \right) &= \frac{1}{3}\ln (x^4 + 12) - \left[ \ln (x + 16) + \frac{1}{2} \ln (x - 3) \right] && \text{Laws of Logarithm } \log_a A^c = C\log_a A\\
\\
\ln \left( \frac{3\sqrt{x^4 + 12}}{(x + 16) \sqrt{x-3}} \right) &= \frac{1}{3}\ln (x^4 + 12) - \ln (x + 16) - \frac{1}{2} \ln (x - 3) && \text{Distributive Property}
\end{aligned}
\end{equation}
$