Using the properties of logarithms, convert the following: \( \log _{6} x^{5} \) \( 5 \log 6 x \) \( 5 \log _{6} x \) \( \log 30 x \) \( 6 \log 5 x \)

To convert the expression \( \log_{6} x^{5} \) using the properties of logarithms, we can apply the power rule, which states that \( \log_{b} (a^{n}) = n \log_{b} a \). ### Step 1: Apply the Power Rule Using the power rule on \( \log_{6} x^{5} \): \[ \log_{6} x^{5} = 5 \log_{6} x \] ### Summary of Conversions 1. \( \log_{6} x^{5} = 5 \log_{6} x \) 2. \( 5 \log 6 x \) is not a direct conversion of \( \log_{6} x^{5} \) but rather a different expression. 3. \( 5 \log_{6} x \) is the same as the result from step 1. 4. \( \log 30 x \) is not directly related to \( \log_{6} x^{5} \). 5. \( 6 \log 5 x \) is also not a direct conversion of \( \log_{6} x^{5} \). ### Final Result The only valid conversion from the original expression \( \log_{6} x^{5} \) is: \[ \log_{6} x^{5} = 5 \log_{6} x \]