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.
\[
\log \left(x y^{2}\right)=\square
\]
$\square \log \square$
Answer
Final Answer: \( \boxed{\log \left(x y^{2}\right) = \log(x) + 2\log(y)} \)
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: \( \boxed{\log \left(x y^{2}\right) = \log(x) + 2\log(y)} \)
