Use the product property of logarithms to write the logarithm as a sum 0 real numbers.
\[
\log _{3}[(m+n) \cdot p]=\square
\]

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Answer

Final Answer: \(\boxed{\log _{3}(m+n) + \log _{3}p}\)

Steps

Step 1 ：The given expression is \(\log _{3}[(m+n) \cdot p]\).

Step 2 ：The product property of logarithms states that the logarithm of a product is the sum of the logarithms of the individual factors.

Step 3 ：Applying this property to the given expression, we can rewrite it as a sum of two logarithms: \(\log _{3}(m+n) + \log _{3}p\).

Step 4 ：Final Answer: \(\boxed{\log _{3}(m+n) + \log _{3}p}\)