Answer
$$\ln \frac{{25{x^3}}}{{{{\left( {{x^2} + 1} \right)}^6}}}$$
Work Step by Step
$$\eqalign{
& 3\left[ {\ln x - 2\ln \left( {{x^2} + 1} \right)} \right] + 2\ln 5 \cr
& {\text{Use the power rule for logarithms }}a\ln b = \ln {b^a} \cr
& 3\left[ {\ln x - \ln {{\left( {{x^2} + 1} \right)}^2}} \right] + \ln {5^2} \cr
& {\text{Use the quotient rule for logarithms }}\ln \left( {\frac{a}{b}} \right) = \ln a - \ln b \cr
& 3\left[ {\ln \frac{x}{{{{\left( {{x^2} + 1} \right)}^2}}}} \right] + \ln {5^2} \cr
& \ln \frac{{{x^3}}}{{{{\left( {{x^2} + 1} \right)}^6}}} + \ln {5^2} \cr
& {\text{Use the product rule for logarithms }}\ln \left( {ab} \right) = \ln a + \ln b \cr
& \ln \frac{{{x^3}}}{{{{\left( {{x^2} + 1} \right)}^6}}} \times {5^2} \cr
& \ln \frac{{25{x^3}}}{{{{\left( {{x^2} + 1} \right)}^6}}} \cr} $$
