Question

which expression is equivalent to \\(\log 18 - \log(p + 2)\\)?\
\\(\bigcirc\\) \\(\log \frac{p + 2}{18}\\)\
\\(\bigcirc\\) \\(\log \frac{18}{p + 2}\\)\
\\(\bigcirc\\) \\(\log \frac{20}{p}\\)\
\\(\bigcirc\\) \\(\log18 \cdot (p + 2)\\)

Explanation:

Step1: Recall the logarithm quotient rule

The quotient rule of logarithms states that $\log a - \log b=\log\frac{a}{b}$, where $a$ and $b$ are positive real numbers and the base of the logarithm is the same (here the base is implied, likely 10 or natural log, but the rule holds for any valid base).

Step2: Apply the rule to the given expression

In the given expression $\log 18-\log(p + 2)$, we can identify $a = 18$ and $b=p + 2$. Applying the quotient rule, we get $\log\frac{18}{p + 2}$.

Answer:

B. $\log\frac{18}{p + 2}$ (assuming the second option is labeled as B, with the expression $\log\frac{18}{p + 2}$)