Simplify expression
[tex]\begin{gathered} \log _{12}\sqrt[3]{\frac{12+x}{144x}}= \\ =\log _{12}(\frac{12+x}{144x})^{\frac{1}{3}}= \\ =\frac{1}{3}\log _{12}(\frac{12+x}{144x})= \\ =\frac{1}{3}(\log _{12}(12+x)-\log _{12}(144x))= \\ =\frac{1}{3}(\log _{12}(12+x)-(\log _{12}(144)+\log _{12}(x)))= \\ =\frac{1}{3}(\log _{12}(12+x)-2+\log _{12}(x))= \\ =\frac{1}{3}\log _{12}(12+x)-\frac{2}{3}+\frac{1}{3}\log _{12}x \end{gathered}[/tex]
So our final answer will be:
[tex]\frac{1}{3}\log _{12}(12+x)-\frac{2}{3}+\frac{1}{3}\log _{12}x[/tex]
