Answer
$$x = \sqrt {3/2} $$
Work Step by Step
$$\eqalign{
& \ln \left( {1/x} \right) + \ln \left( {2{x^3}} \right) = \ln 3 \cr
& {\text{use the product property for logarithms}} \cr
& \ln \left( {\frac{{2{x^3}}}{x}} \right) = \ln 3 \cr
& {\text{simplify}} \cr
& \ln \left( {2{x^2}} \right) = \ln 3 \cr
& {\text{then}}{\text{,}} \cr
& 2{x^2} = 3 \cr
& {x^2} = 3/2 \cr
& x = \sqrt {3/2} \cr} $$