Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$6 \log _ { a } q - 3 \log _ { a } p ^ { 2 }$
A) $\log _ { a } \left( \frac { q ^ { 6 } } { p ^ { 6 } } \right)$
B) $\frac { \log _ { a } q ^ { 6 } } { \log _ { a } p ^ { 6 } }$
C) $\log _ { a } \left( \frac { q ^ { 6 } } { p ^ { 5 } } \right)$
D) $\log _ { a } \left( \frac { 6 q } { 3 p ^ { 2 } } \right)$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $6\log_a q = \log_a q^6$ and $3\log_a p^2 = \log_a (p^2)^3 = \log_a p^6$. Subtracting these gives $\log_a q^6 - \log_a p^6 = \log_a \frac{q^6}{p^6}$.

Write the Expression as a Single Logarithm with Coefficient 1 a≠1 and b≠1a \neq 1 \text { and } b \neq 1a=1 and b=1

Write the Expression as a Single Logarithm with Coefficient 1 $a \neq 1 \text { and } b \neq 1$