Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x, \log y$, and $\log z$. \[ \log \frac{x z^{4}}{y} \]

Step 1 ：Given the expression \(\log \frac{x z^{4}}{y}\)

Step 2 ：Apply the properties of logarithms to expand the expression: \(\log \frac{x z^{4}}{y} = \log x + \log z^{4} - \log y\)

Step 3 ：Apply the property of logarithms \(\log(a^n) = n \log a\) to \(\log z^{4}\) to get: \(\log x + 4\log z - \log y\)

Step 4 ：Final Answer: \(\boxed{\log x + 4\log z - \log y}\)