Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 3 } \left( \frac { \sqrt { x } } { 27 } \right)$
A) $9 - \frac { 1 } { 2 } \log _ { 3 } x$
B) $- 3 \log _ { 3 } x$
C) $\log _ { 3 } x - 3$
D) $\frac { 1 } { 2 } \log _ { 3 } x - 3$

Question

Quizplus · Accepted Answer

The expression can be rewritten using logarithm properties: $\log_3(\sqrt{x}) - \log_3(27) = \frac{1}{2}\log_3(x) - 3$, since $\sqrt{x} = x^{1/2}$ and $27 = 3^3$.

Write as the Sum And/or Difference of Logarithms log⁡3(x27)\log _ { 3 } \left( \frac { \sqrt { x } } { 27 } \right)log3​(27x​​)

Write as the Sum And/or Difference of Logarithms $\log _ { 3 } \left( \frac { \sqrt { x } } { 27 } \right)$