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 conversion 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 is because the base of the logarithm corresponds to the base of the exponent, the argument of the logarithm is the result of the exponential expression, and the value of the logarithm is the exponent.

Change the Exponential Expression to an Equivalent Expression Involving a Logarithm