Problem

Use the product property of logarithms to write the logarithm as a sum of logarithms. Then simplify if possible. Assume that all variable expressions represent positive real numbers. \[ \log (17 p q)=\square \] $\square \circ \square$

Solution

Step 1 :Given the logarithmic expression \(\log (17 p q)\).

Step 2 :The product property of logarithms states that the logarithm of a product is the sum of the logarithms of its factors. Therefore, we can apply this property to the given logarithm to write it as a sum of logarithms.

Step 3 :So, \(\log (17 p q)\) can be written as \(\log (17)+\log (p)+\log (q)\).

Step 4 :Therefore, the final simplified form of the given logarithmic expression is \(\boxed{\log (17)+\log (p)+\log (q)}\).

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