Question Watch Video Expand the logarithm fully using the properties of logs. Express the final answer in terms of $\log x, \log y$, and $\log z$. \[ \log \frac{y}{x^{4} \sqrt{z^{5}}} \] Answer Attempt 1 out of 2

Step 1 ：Given the expression is a logarithm of a fraction, we can use the properties of logarithms to simplify this expression. The logarithm of a quotient is the difference of the logarithms. Also, the logarithm of a product is the sum of the logarithms. And the logarithm of a power is the product of the exponent and the logarithm of the base. So, we can apply these properties to expand the given logarithm.

Step 2 ：Using these properties, we can rewrite the expression as \(-4\log x + \log y - \frac{5}{2}\log z\).

Step 3 ：The final expanded form of the given logarithm is \(\boxed{-4\log x + \log y - \frac{5}{2}\log z}\).