Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\left( \log _ { a } x - \log _ { a } y \right) + 3 \log _ { a } z$
A) $\log _ { a } \frac { x } { z ^ { 3 } y }$
B) $\log _ { a } x z ^ { 3 } y$
C) $\log _ { a } \frac { 3 x z } { y }$
D) $\log _ { a } \frac { x z ^ { 3 } } { y }$

Question

Quizplus · Accepted Answer

Using the logarithm rules, $\log_a x - \log_a y = \log_a \frac{x}{y}$ and $3\log_a z = \log_a z^3$, combining these gives $\log_a \frac{xz^3}{y}$.

Express as the Logarithm of a Single Expression (log⁡ax−log⁡ay)+3log⁡az\left( \log _ { a } x - \log _ { a } y \right) + 3 \log _ { a } z(loga​x−loga​y)+3loga​z

Express as the Logarithm of a Single Expression $\left( \log _ { a } x - \log _ { a } y \right) + 3 \log _ { a } z$