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


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