Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log 8 \left( \frac { \sqrt { 11 } } { 12 } \right)$
A) $\frac { 1 } { 2 } \log 811 - \log _ { 8 } 12$
B) $\log 8 \sqrt { 11 } + \log 812$
C) $\frac { \frac { 1 } { 2 } \log _ { 8 } 11 } { \log _ { 8 } 12 }$
D) $\sqrt { \log _ { 8 } 11 } - \log _ { 8 } 12$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\log_8 \left( \frac { \sqrt { 11 } } { 12 } \right)$ can be rewritten as the difference of two logarithms: $\log_8(\sqrt{11}) - \log_8(12)$. Further simplifying, $\log_8(\sqrt{11})$ can be written as $\frac{1}{2}\log_8(11)$, leading to the correct answer: $\frac { 1 } { 2 } \log_8 11 - \log_8 12$.

Use the Properties of Logarithms to Rewrite the Expression log⁡8(1112)\log 8 \left( \frac { \sqrt { 11 } } { 12 } \right)log8(1211​​)

Use the Properties of Logarithms to Rewrite the Expression $\log 8 \left( \frac { \sqrt { 11 } } { 12 } \right)$