Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { 6 } \left( \frac { 4 \sqrt { 6 } } { 11 } \right)$
$\log _ { 6 } 4 + \frac { 1 } { 2 } \log _ { 6 } 6$
A) $\log _ { 6 } 4 + \sqrt { \log _ { 6 } 6 } - \log _ { 6 } 11$
B) $\frac { \log _ { 6 } 11 } { }$
C) $\left( \log _ { 6 } 4 \right) \left( \frac { 1 } { 2 } \log _ { 6 } 6 \right) - \log _ { 6 } 11$
D) $\log _ { 6 } 4 + \frac { 1 } { 2 } \log _ { 6 } 6 - \log _ { 6 } 11$

Question

Quizplus · Accepted Answer

The expression can be simplified using the properties of logarithms: the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$ and the power rule $\log_b M^p = p \log_b M$. The square root of 6 can be written as $6^{1/2}$, applying the power rule gives $\frac{1}{2} \log_6 6$. Combining these rules simplifies the original expression to $\log_6 4 + \frac{1}{2} \log_6 6 - \log_6 11$.

Use the Properties of Logarithms to Rewrite the Expression log⁡6(4611)\log _ { 6 } \left( \frac { 4 \sqrt { 6 } } { 11 } \right)log6​(1146​​)

Use the Properties of Logarithms to Rewrite the Expression $\log _ { 6 } \left( \frac { 4 \sqrt { 6 } } { 11 } \right)$