Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 9 } } \right)$
A) $\log _ { \mathrm { b } } \mathrm { x } + 5 \log _ { \mathrm { b } } \mathrm { y } - 9 \log _ { \mathrm { b } } \mathrm { z }$
B) $\log _ { b } x + 5 \log _ { b } y + 9 \log _ { b } z$
C) $\log _ { b } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 5 } - \log _ { \mathrm { b } } \mathrm { z } ^ { 9 }$
D) $\log _ { b } \mathrm { x } + \log _ { \mathrm { b } } \mathrm { y } ^ { 5 } + \log _ { \mathrm { b } ^ { \mathrm { z } } } 9$

Question

Quizplus · Accepted Answer

The correct expansion uses the properties of logarithms: the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$ and the power rule $\log_b M^n = n \log_b M$, resulting in $\log_b x + 5\log_b y - 9\log_b z$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much