Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { 4 } \left( \frac { 16 } { x } \right)$
A) $8 - \log _ { 4 } x$
B) $- 2 \log _ { 4 } x$
C) $2 - \log _ { 4 } x$
D) $\frac { 2 } { x }$

Question

Quizplus · Accepted Answer

The expression can be expanded using the quotient rule of logarithms, $\log_b \frac{M}{N} = \log_b M - \log_b N$, and the fact that $\log_4 16 = 2$ because $4^2 = 16$. Thus, $\log_4 \frac{16}{x} = \log_4 16 - \log_4 x = 2 - \log_4 x$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much