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

Answer

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Answer

Final Answer: $\boxed{\log x + 4\log z - \log y}$

Steps

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: $\boxed{\log x + 4\log z - \log y}$