Write the exponential equation in logarithmic form. $2 ^ { - 2 } = \frac { 1 } { 4 }$
A) $\log _ { 4 } \frac { 1 } { 2 } = - 2$
B) $\log _ { 2 } \frac { 1 } { 4 } = 2$
C) $\log _ { 2 } 4 = 2$
D) $\log _ { 2 } \frac { 1 } { 4 } = - 2$
E) $\log _ { 2 } 4 = - 2$

Question

Write the exponential equation in logarithmic form. $2 ^ { - 2 } = \frac { 1 } { 4 }$ 
A) $\log _ { 4 } \frac { 1 } { 2 } = - 2$
B) $\log _ { 2 } \frac { 1 } { 4 } = 2$
C) $\log _ { 2 } 4 = 2$
D) $\log _ { 2 } \frac { 1 } { 4 } = - 2$
E) $\log _ { 2 } 4 = - 2$

Quizplus · Accepted Answer

The exponential equation $2^{-2} = \frac{1}{4}$ can be rewritten in logarithmic form as $\log_{2}\frac{1}{4} = -2$, which matches choice D. This is because the base of the logarithm matches the base of the exponent, the argument of the logarithm is the result of the exponentiation, and the value of the logarithm is the exponent itself.

Write the Exponential Equation in Logarithmic Form 2−2=142 ^ { - 2 } = \frac { 1 } { 4 }2−2=41​

Write the Exponential Equation in Logarithmic Form $2 ^ { - 2 } = \frac { 1 } { 4 }$