Rewrite the logarithmic equation $\log _ { 2 } \frac { 1 } { 4 } = - 2$ in exponential form.
A) $2 ^ { 4 } = - 2$
B) $2 ^ { 1 / 4 } = - 2$
C) $2 ^ { - 2 } = \frac { 1 } { 4 }$
D) $\left( \frac { 1 } { 4 } \right) ^ { - 2 } = 2$

E) $2 ^ { - 2 } = - \frac { 1 } { 4 }$

Question

Rewrite the logarithmic equation $\log _ { 2 } \frac { 1 } { 4 } = - 2$ in exponential form.
A) $2 ^ { 4 } = - 2$
B) $2 ^ { 1 / 4 } = - 2$
C) $2 ^ { - 2 } = \frac { 1 } { 4 }$
D) $\left( \frac { 1 } { 4 } \right) ^ { - 2 } = 2$

E) $2 ^ { - 2 } = - \frac { 1 } { 4 }$

Quizplus · Accepted Answer

The logarithmic equation $\log_2 \frac{1}{4} = -2$ means that $2^{-2}=\frac{1}{4}$. Therefore, the exponential form of the equation is $2^{-2}=\frac{1}{4}$. The other answer choices do not correctly represent the relationship between the logarithmic and exponential forms of the equation.

Rewrite the Logarithmic Equation log⁡214=−2\log _ { 2 } \frac { 1 } { 4 } = - 2log2​41​=−2

Rewrite the Logarithmic Equation $\log _ { 2 } \frac { 1 } { 4 } = - 2$