Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 2 } \left( \frac { \sqrt { y } } { 16 } \right)$
A) $\frac { 1 } { 2 } \log _ { 2 } y - \log _ { 2 } 16$
B) $\log _ { 2 } \sqrt { y } - \log _ { 2 } 16$
C) $\log _ { 2 } \sqrt { y } - 4 \log _ { 2 } 2$
D) $\frac { 1 } { 2 } \log _ { 2 } y - 4$

Question

Quizplus · Accepted Answer

The expression can be expanded using the properties of logarithms: $\log _ { 2 } \left( \frac { \sqrt { y } } { 16 } \right) = \log _ { 2 } \sqrt { y } - \log _ { 2 } 16$. Since $\sqrt{y} = y^{1/2}$, $\log _ { 2 } \sqrt { y } = \frac{1}{2} \log _ { 2 } y$. Also, $\log _ { 2 } 16 = 4$ because $16 = 2^4$. Thus, the expression simplifies to $\frac{1}{2} \log _ { 2 } y - 4$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much