Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { b } \left( \frac { x y ^ { 4 } } { z ^ { 2 } } \right)$
A) $\log _ { b } x + 4 \log _ { b } y - 2 \log _ { b } z$
B) $\log _ { b } x + 4 \log _ { b } y + 2 \log _ { b ^ { z } }$
C) $\log _ { b } x + \log _ { b } y ^ { 4 } - \log _ { b } z ^ { 2 }$
D) $\log _ { b } x + \log _ { b } y ^ { 4 } + \log _ { b } z ^ { 2 }$

Question

Quizplus · Accepted Answer

The expression $\log _ { b } \left( \frac { x y ^ { 4 } } { z ^ { 2 } } \right)$ can be expanded using the properties of logarithms: the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$ and the power rule $\log_b M^n = n \log_b M$. This results in $\log _ { b } x + 4 \log _ { b } y - 2 \log _ { b } z$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much