Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 6 } ( 7 \cdot 3 )$
A) $\log _ { 6 } 21$
B) $\log _ { 6 } 7 + \log _ { 6 } 3$
C) $\left( \log _ { 6 } 7 \right) \left( \log _ { 6 } 3 \right)$
D) $\log _ { 6 } 7 - \log _ { 6 } 3$

Question

Quizplus · Accepted Answer

The property of logarithms that applies here is $\log_b(xy) = \log_b(x) + \log_b(y)$, which directly leads to the expansion $\log_6(7\cdot3) = \log_6 7 + \log_6 3$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much