Question

expand the logarithm. assume all expressions exist and are well - defined. write your answer as a sum or difference of common logarithms or multiples of common logarithms. the inside of each logarithm must be a distinct constant or variable. \\(\log \frac{17}{wv}\\)

Explanation:

Step1: Apply the Quotient Rule of Logarithms

The quotient rule of logarithms states that $\log \frac{a}{b} = \log a - \log b$. For the given logarithm $\log \frac{17}{wv}$, we can apply this rule.
So, $\log \frac{17}{wv} = \log 17 - \log (wv)$

Step2: Apply the Product Rule of Logarithms

The product rule of logarithms states that $\log (ab) = \log a + \log b$. Applying this to $\log (wv)$, we get $\log (wv) = \log w + \log v$.

Step3: Substitute Back

Substituting $\log (wv) = \log w + \log v$ back into the expression from Step1, we have:
$\log 17 - (\log w + \log v) = \log 17 - \log w - \log v$

Answer:

$\log 17 - \log w - \log v$