Write as the sum and/or difference of logarithms. Express powers as factors. \( \log _{6}\left(x z^{3}\right) \)

To express \( \log_{6}(xz^{3}) \) as the sum and/or difference of logarithms, you can use the properties of logarithms. First, apply the product rule: \[ \log_{6}(xz^{3}) = \log_{6}(x) + \log_{6}(z^{3}). \] Next, apply the power rule to express \( z^{3} \) as a factor: \[ \log_{6}(z^{3}) = 3\log_{6}(z). \] Putting it all together, you get: \[ \log_{6}(xz^{3}) = \log_{6}(x) + 3\log_{6}(z). \]