Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
-$3 \log _ { a } x - 9 \log _ { a } z ^ { 2 }$
A) $\frac { \log _ { a } x ^ { 3 } } { \log _ { a } z ^ { 18 } }$
B) $\log _ { a } \left( \frac { x ^ { 3 } } { z ^ { 11 } } \right)$
C) $\log _ { a } \left( \frac { x ^ { 3 } } { z ^ { 18 } } \right)$
D) $\log _ { a } \left( \frac { 3 x } { 9 z ^ { 2 } } \right)$

Question

Quizplus · Accepted Answer

The expression can be simplified using logarithm properties: $3 \log_a x = \log_a x^3$ and $9 \log_a z^2 = \log_a (z^2)^9 = \log_a z^{18}$. Combining these using subtraction of logarithms, which corresponds to division inside the log, gives $\log_a \left( \frac{x^3}{z^{18}} \right)$.

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