Rewrite the exponential equation $5 ^ { - 3 } = \frac { 1 } { 125 }$ in logarithmic form.
A) $\log _ { 5 } 125 = - 3$
B) $\log _ { 125 } 5 = - 3$
C) $\log _ { 3 } 125 = - 3$
D) $\log _ { 5 } \frac { 1 } { 125 } = - 3$
E) $\log _ { 5 } \frac { 1 } { 125 } = 3$

Question

Quizplus · Accepted Answer

The logarithmic form of $5^{-3} = \frac{1}{125}$ is $\log_{5}\frac{1}{125} = -3$, which matches choice D. 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 itself.

Rewrite the Exponential Equation 5−3=11255 ^ { - 3 } = \frac { 1 } { 125 }5−3=1251​

Rewrite the Exponential Equation $5 ^ { - 3 } = \frac { 1 } { 125 }$