Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$\log _ { 4 } \frac { y } { 2 }$

A) $2 \log _ { 4 } y$

B) $y - \log _ { 4 } 2$

C) $\log _ { 4 } y - 2$

D) $\frac { \log _ { 4 } y } { 2 }$

E) $\log _ { 4 } y - \log _ { 4 } 2$

Question

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$\log _ { 4 } \frac { y } { 2 }$

A) $2 \log _ { 4 } y$

B) $y - \log _ { 4 } 2$

C) $\log _ { 4 } y - 2$

D) $\frac { \log _ { 4 } y } { 2 }$

E) $\log _ { 4 } y - \log _ { 4 } 2$

Quizplus · Accepted Answer

We can use the property of logarithms that states:
$$\log_b\frac{a}{c}=\log_ba-\log_bc$$
to rewrite $\log_4\frac{y}{2}$ as:
$$\log_4y-\log_42$$
which is equivalent to $\log_4y-\frac{1}{2}$, so the answer is $\boxed{	ext{(E) }\log_4y-\log_42}$.

Use the Properties of Logarithms to Expand the Expression as a Sum