Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 3 } \left( \frac { 9 } { \sqrt { x - 1 } } \right)$
A) $2 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 )$
B) $2 \log _ { 3 } 3 - \frac { 1 } { 2 } \log _ { 3 } ( x - 1 )$
C) $\log _ { 3 } 9 - \log _ { 3 } \sqrt { x - 1 }$
D) $2 - \log _ { 3 } \sqrt { x - 1 }$

Question

Quizplus · Accepted Answer

The expression can be expanded using the properties of logarithms: $\log_3(9) - \log_3(\sqrt{x-1}) = 2 - \frac{1}{2}\log_3(x-1)$, since $\log_3(9) = 2$ and $\log_3(\sqrt{x-1}) = \frac{1}{2}\log_3(x-1)$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much