Problem
Question Use the Product Rule of Logarithms to write the completely expanded expression equivalent to $\log _{5}(3 x+6 y)$. Make sure to use parenthesis around your logarithm functions $\log (x+y)$. Note: If you are using log you need to type it in and then use the subscript button $\left(x_{\square}\right)$ on the keypad. There is no log button. Provide your answer below: II FEEDBACK MORE INSTRUCTION SUBMIT Content attribution
Solution
Step 1 ：The Product Rule of Logarithms states that the logarithm of a product is the sum of the logarithms of its factors. In this case, we have $\log _{5}(3 x+6 y)$, which is not a product, so we can't directly apply the Product Rule.
Step 2 ：However, we can factor out a 3 from the expression inside the logarithm to get $\log _{5}(3(x + 2y))$. Now we have a product inside the logarithm, so we can apply the Product Rule.
Step 3 ：The Product Rule will allow us to split the logarithm of the product into the sum of the logarithms of the factors.
Step 4 ：Final Answer: \(\boxed{\log _{5}(3) + \log _{5}(x + 2y)}\)
