Express as a single logarithm.
-$$\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z$$
A) $\log _ { a } \frac { x } { z ^ { 5 } y }$
B) $\log _ { \mathrm { a } } \frac { 5 \mathrm { xz } } { \mathrm { y } }$
C) $\log _ { a } \frac { x z ^ { 5 } } { y }$
D) $\log _ { \mathrm { a } } \mathrm { xz } ^ { 5 } \mathrm { y }$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $\log_a x - \log_a y = \log_a \frac{x}{y}$ and $5\log_a z = \log_a z^5$. Combining these gives $\log_a \frac{xz^5}{y}$.

Express as a Single Logarithm (log⁡ax−log⁡ay)+5log⁡az\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z(loga​x−loga​y)+5loga​z

Express as a Single Logarithm $\left( \log _ { a } x - \log _ { a } y \right) + 5 \log _ { a } z$