Write as a logarithm of a single expression.
-$\frac { 1 } { 2 } \left( \log _ { 6 } ( r - 3 ) - \log _ { 6 } r \right)$
A) $\log _ { 6 } \frac { r - 3 } { \sqrt { r } }$
B) $\log _ { 6 } \frac { \sqrt { r - 3 } } { r }$
C) $\log _ { 6 } \sqrt { \frac { r - 3 } { r } }$
D) $\log _ { 6 } \sqrt { \frac { r - 3 } { 2 r } }$

Question

Quizplus · Accepted Answer

The expression can be simplified using the logarithm properties: $\frac{1}{2}(\log_6(r-3) - \log_6 r)$ can be rewritten as $\log_6 \sqrt{\frac{r-3}{r}}$ by combining the logs into a single log (using the quotient rule) and then applying the power rule to account for the $\frac{1}{2}$ factor, which corresponds to taking the square root.

Write as a Logarithm of a Single Expression 12(log⁡6(r−3)−log⁡6r)\frac { 1 } { 2 } \left( \log _ { 6 } ( r - 3 ) - \log _ { 6 } r \right)21​(log6​(r−3)−log6​r)

Write as a Logarithm of a Single Expression $\frac { 1 } { 2 } \left( \log _ { 6 } ( r - 3 ) - \log _ { 6 } r \right)$