Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
-$$\left( \log _ { a } x - \log _ { a } y \right) + 6 \log _ { a } z$$
A) $\log _ { a } \left( \frac { x z ^ { 6 } } { y } \right)$
B) $\log _ { a } \left( \frac { 6 x z } { y } \right)$
C) $\log _ { a } \left( \frac { x } { z ^ { 6 } y } \right)$
D) $\log _ { a } \left( x + z ^ { 6 } - y \right)$

Question

Quizplus · Accepted Answer

The expression simplifies to $\log_a \left( \frac{xz^6}{y} \right)$ by using the logarithm properties: $\log_a b - \log_a c = \log_a \left(\frac{b}{c}\right)$ and $m \log_a n = \log_a n^m$.

Write the Expression as a Single Logarithm with Coefficient 1 (log⁡ax−log⁡ay)+6log⁡az\left( \log _ { a } x - \log _ { a } y \right) + 6 \log _ { a } z(loga​x−loga​y)+6loga​z

Write the Expression as a Single Logarithm with Coefficient 1 $\left( \log _ { a } x - \log _ { a } y \right) + 6 \log _ { a } z$