College Algebra, Chapter 5, 5.3, Section 5.3, Problem 38

Expand the expression $\displaystyle \ln \frac{3x^2}{(x + 1)^{10}}$, using Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\ln \frac{3x^2}{(x + 1)^{10}} =& \ln 3x^2 - \ln (x + 1)^{10}
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
\ln \frac{3x^2}{(x + 1)^{10}} =& \ln 3 + \ln x^2 - \ln (x + 1)^{10}
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
\\
\\
\ln \frac{3x^2}{(x + 1)^{10}} =& \ln 3 + 2 \ln x - 10 \ln (x + 1)
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A

\end{aligned}
\end{equation}
$