Question

which expression is equivalent to \\(\log_{3} \frac{c}{9}\\)? \\(\log_{3} c - \log_{3} (9)\\) \\(\log_{3} c + \log_{3} (9)\\) \\(\log_{3} (9) - \log_{3} (c)\\) \\(\log_{3} (9) + \log_{3} (c)\\)

Explanation:

Step1: Recall Logarithm Quotient Rule

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

Step2: Apply the Rule to $\log_3 \frac{c}{9}$

Here, $b = 3$, $m = c$, and $n = 9$. Applying the quotient rule, we get:
$\log_3 \frac{c}{9} = \log_3 c - \log_3 9$

Answer:

$\log_3 c - \log_3 (9)$ (the first option)