Question

which expression is equivalent to \\(\log 18 - \log (p + 2)\\)?\
\\(\log_{p + 2} \frac{18}{p + 2}\\)\
\\(\log 18 \cdot (p + 2)\\)\
\\(\log_p \frac{20}{p}\\)\
\\(\log \frac{p + 2}{18}\\)

Explanation:

Step1: Recall Logarithm Quotient Rule

The quotient rule of logarithms states that $\log_b \frac{m}{n} = \log_b m - \log_b n$ for $b>0, b
eq1, m>0, n>0$.

Step2: Apply the Rule to Given Expression

We have the expression $\log 18 - \log (p + 2)$. Using the quotient rule in reverse (since we want to combine the two logarithms into one), we can rewrite it as $\log \frac{18}{p + 2}$.

Answer:

$\log_{} \frac{18}{p + 2}$ (the first option among the given choices, assuming the first option is $\log \frac{18}{p + 2}$)