Answer
$2+3\log_{6}x $
Work Step by Step
Basic logarihmic properties:$ \left\{\begin{array}{l}
\log_{b}1=0\\
\log_{b}b=1\\
\log_{b}b^{x}=x\\
b^{\log_{b}}x=x
\end{array}\right.$
Rules:
The Product Rule: $\log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$
The Quotient Rule: $\displaystyle \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
The Power Rule: $\log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
---
$\log_{6}(36\cdot x^{3})=\qquad $... apply Product Rule
$=\log_{6}36+\log_{6}x^{3}=\qquad $... recognize 36 as $6^{2}$
$=\log_{6}6^{2}+\log_{6}x^{3}=\qquad $... apply Power Rule
$=2\log_{6}6+3\log_{6}x=\qquad $... apply $\log_{b}b=1$
$=2\cdot 1+3\log_{6}x $
= $2+3\log_{6}x $
