Simplify the expression without using a calculator.
-$\log _ { 6 } \sqrt { \frac { 1 } { 216 } }$
A) $- \frac { 3 } { 2 }$
B) $- \frac { 2 } { 3 }$
C) $\frac { 3 } { 2 }$
D) $\frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

The expression simplifies as follows: $\log_6 \sqrt{\frac{1}{216}} = \log_6 (216^{-\frac{1}{2}}) = \log_6 (6^{-3})^{\frac{1}{2}} = \frac{1}{2} \cdot (-3) \log_6 6 = -\frac{3}{2}$, since $216 = 6^3$ and $\log_6 6 = 1$.

Simplify the Expression Without Using a Calculator log⁡61216\log _ { 6 } \sqrt { \frac { 1 } { 216 } }log6​2161​​

Simplify the Expression Without Using a Calculator $\log _ { 6 } \sqrt { \frac { 1 } { 216 } }$