Write the expression as the sum or difference of single logarithms.
-$\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$
A) $\frac { 1 } { 4 } \log _ { 5 } x + \frac { 1 } { 3 } \log _ { 5 } y - 2 \log _ { 5 } z$
B) $\frac { 4 } { 5 } \log _ { 5 } x + \frac { 3 } { 5 } \log _ { 5 } y - \frac { 2 } { 5 } \log _ { 5 } z$
C) $\frac { 1 } { 4 } \log _ { 5 } x \cdot \frac { 1 } { 3 } \log _ { 5 } y \div 2 \log _ { 5 } z$
D) $4 \log _ { 5 } x + 3 \log _ { 5 } y - 2 \log _ { 5 } z$

Question

Quizplus · Accepted Answer

The expression can be rewritten using logarithm properties: the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$, the product rule $\log_b (MN) = \log_b M + \log_b N$, and the power rule $\log_b M^k = k \log_b M$. Applying these rules, we get $\frac{1}{4} \log_5 x + \frac{1}{3} \log_5 y - 2 \log_5 z$.

Write the Expression as the Sum or Difference of Single log⁡5x4y3z2\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }log5​z24x​3y​​

Write the Expression as the Sum or Difference of Single $\log _ { 5 } \frac { \sqrt [ 4 ] { x } \sqrt [ 3 ] { y } } { z ^ { 2 } }$