Use properties of logarithms to expand the logarithmic expression as much as possible.
-$$\log _ { 3 } ( 2 \cdot 11 )$$
A) $\log _ { 3 } 2 + \log _ { 3 } 11$
B) $\log _ { 3 } 22$
C) $\log _ { 3 } 2 - \log _ { 3 } 11$
D) $\left( \log _ { 3 } 2 \right) \left( \log _ { 3 } 11 \right)$

Question

Quizplus · Accepted Answer

The property of logarithms that applies here is the product rule: $\log_b(xy) = \log_b(x) + \log_b(y)$. Therefore, $\log_3(2 \cdot 11)$ expands to $\log_3(2) + \log_3(11)$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much