Express as the sum or difference of logarithms.
\[
\log _{5} 3 y
\]
Final Answer: \(\boxed{\log _{5} 3 + \log _{5} y}\)
Step 1 :The given expression is a logarithm of a product. According to the properties of logarithms, the logarithm of a product can be expressed as the sum of the logarithms of the individual factors.
Step 2 :In this case, the product is 3y, so we can express this as the sum of the logarithms of 3 and y. The base of the logarithm remains the same.
Step 3 :Using the properties of logarithms, we can rewrite the expression \(\log _{5} 3 y\) as \(\log _{5} 3 + \log _{5} y\).
Step 4 :Final Answer: \(\boxed{\log _{5} 3 + \log _{5} y}\)