TeX source:

\begin{aligned} \log _{6}\left(\frac{64 x^{3}(4 x+1)}{(2 x-1)}\right) &=\log _{6} 64+\log _{6} x^{3}+\log _{6}(4 x+1)-\log _{6}(2 x-1) & & \text { Apply the Quotient Rule. }\\ &=\log _{6} 2^{6}+\log _{6} x^{3}+\log _{6}(4 x+1)-\log _{6}(2 x-1) & & \text { Simplify by writing } 64 \text { as } 2^{6} \text {. }\\ &=6 \log _{6} 2+3 \log _{6} x+\log _{6}(4 x+1)-\log _{6}(2 x-1) & & \text { Apply the Power Rule. } \end{aligned}