Change the exponential expression to an equivalent expression involving a logarithm.
-$$3 ^ { - 2 } = \frac { 1 } { 9 }$$
A) $\log _ { - 2 } \frac { 1 } { 9 } = 3$
B) $\log _ { 1 / 9 } 3 = - 2$
C) $\log _ { 3 } \frac { 1 } { 9 } = - 2$
D) $\log _ { 3 } - 2 = \frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

The correct transformation from the exponential form $3^{-2} = \frac{1}{9}$ to a logarithmic form is $\log_{3}\frac{1}{9} = -2$, which matches choice C. This follows the logarithmic form $\log_{b}a = c$ equivalent to the exponential form $b^c = a$.

Change the Exponential Expression to an Equivalent Expression Involving a Logarithm