Use properties of logarithms to expand the following expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
\[
\log _{6}\left(36 x^{3}\right)
\]

Answer

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Answer

\(\boxed{2 + 3\log _{6}(x)}\)

Steps

Step 1 ：\(\log _{6}\left(36 x^{3}\right) = \log _{6}(36) + \log _{6}(x^{3})\)

Step 2 ：\(\log _{6}(36) + \log _{6}(x^{3}) = \log _{6}(36) + 3\log _{6}(x)\)

Step 3 ：\(\log _{6}(36) + 3\log _{6}(x) = 2 + 3\log _{6}(x)\)

Step 4 ：\(\boxed{2 + 3\log _{6}(x)}\)