Answer
$$\ln \left( {\frac{{{{\left( {x + 1} \right)}^2}\root 3 \of x }}{{\cos x}}} \right)$$
Work Step by Step
$$\eqalign{
& 2\ln \left( {x + 1} \right) + \frac{1}{3}\ln x - \ln \left( {\cos x} \right) \cr
& {\text{use the power property for logarithms }}\log {a^n} = n\log a \cr
& = \ln {\left( {x + 1} \right)^2} + \ln {x^{1/3}} - \ln \left( {\cos x} \right) \cr
& {\text{use the quotient property for logarithms}} \cr
& = \ln {\left( {x + 1} \right)^2} + \ln \left( {\frac{{{x^{1/3}}}}{{\cos x}}} \right) \cr
& {\text{use the product property for logarithms}} \cr
& = \ln \left( {\frac{{{{\left( {x + 1} \right)}^2}\root 3 \of x }}{{\cos x}}} \right) \cr} $$
