Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $$a \neq 1 \text { and } b \neq 1$$
-$$\frac { 3 } { 4 } \log _ { a } \left( p ^ { 2 } q ^ { 8 } \right) - \frac { 1 } { 2 } \log _ { a } \left( p ^ { 5 } q ^ { 2 } \right)$$
A) $\log _ { a } \left( p ^ { 4 } q ^ { 7 } \right)$
B) $\log _ { a } \left( \frac { q ^ { 5 } } { p } \right)$
C) $\log _ { a } \left( \frac { 3 } { 4 } p ^ { 2 } q ^ { 8 } - \frac { 1 } { 2 } p ^ { 5 } q ^ { 2 } \right)$
D) $\log _ { a } \left( \frac { 3 q ^ { 6 } } { 2 p ^ { 3 } } \right)$

Question

Quizplus · Accepted Answer

The expression simplifies using logarithm properties: the first term's coefficients become exponents, and subtraction of logs translates to division. Simplifying gives $\log_a \left( \frac{p^{(3/4)*2}q^{(3/4)*8}}{p^{(1/2)*5}q^{(1/2)*2}} \right) = \log_a \left( \frac{p^{3/2}q^{6}}{p^{5/2}q} \right) = \log_a \left( \frac{q^{5}}{p} \right)$.

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 $a \neq 1 \text { and } b \neq 1$