Use the properties of logarithms to expand $\log \left(z y^{7}\right)$. Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. \[ \log \left(z y^{7}\right)= \]

Step 1 ：Given the logarithmic expression \(\log \left(z y^{7}\right)\).

Step 2 ：Use the properties of logarithms to expand the expression. The properties state that \(\log(ab) = \log(a) + \log(b)\) and \(\log(a^n) = n\log(a)\).

Step 3 ：Applying these properties, the expression \(\log \left(z y^{7}\right)\) can be expanded as \(7\log(y) + \log(z)\).

Step 4 ：Final Answer: \(\log \left(z y^{7}\right) = \boxed{7\log(y) + \log(z)}\)