Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$
A) $\frac { 1 } { 4 } \log _ { 3 } x - 1$
B) $\log _ { 3 } x - \log _ { 3 } 4 - 1$
C) $\frac { 1 } { 4 } \log _ { 3 } x - \frac { 1 } { 4 }$
D) $\log _ { 3 } \sqrt [ 4 ] { x } - \log _ { 3 } \sqrt [ 4 ] { 3 }$

Question

Quizplus · Accepted Answer

The given expression can be rewritten using logarithm properties: $\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } } = \log _ { 3 } (x^{1/4}) - \log _ { 3 } (3^{1/4})$. Simplifying further, we get $\frac { 1 } { 4 } \log _ { 3 } x - \frac { 1 } { 4 }$, because $\log _ { 3 } 3 = 1$.

Write the Logarithm as a Sum or Difference of Logarithms log⁡3x34\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }log3​43x​​

Write the Logarithm as a Sum or Difference of Logarithms $\log _ { 3 } \sqrt [ 4 ] { \frac { x } { 3 } }$