Problem

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

Solution

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

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Source: https://solvelyapp.com/problems/jBYwiGDvRc/

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