Expanding a logarithmic expression: Problem type 1 Use the properties of logarithms to expand $\log \left(x y^{2}\right)$. Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. \[ \log \left(x y^{2}\right)=\square \] $\square \log \square$

Step 1 ：The problem is asking to expand the logarithmic expression \( \log \left(x y^{2}\right) \).

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

Step 3 ：We can use these properties to expand the given expression.

Step 4 ：Applying the properties, we get \( \log \left(x y^{2}\right) = \log(x) + 2\log(y) \).

Step 5 ：Final Answer: \( \boxed{\log \left(x y^{2}\right) = \log(x) + 2\log(y)} \)