Problem
Use the properties of logarithms to expand $\log \left(x^{6} z\right)$. Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. \[ \log \left(\begin{array}{c} x^{6} \\ z \end{array}\right)=\prod \]
Solution
Step 1 ：Use the properties of logarithms to expand $\log \left(x^{6} z\right)$.
Step 2 ：Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive.
Step 3 ：Final Answer: $\boxed{6 \log(x) + \log(z)}$
