Change the exponential expression to an equivalent expression involving a logarithm.
-$$32 ^ { 2 / 5 } = 4$$
A) $\log _ { 4 } 32 = \frac { 2 } { 5 }$
B) $\log _ { 32 } 4 = \frac { 2 } { 5 }$
C) $\log _ { 2 } 32 = \frac { 2 } { 5 }$
D) $\frac { \log _ { 5 } 4 } { \log _ { 2 } 32 } = 32$

Question

Quizplus · Accepted Answer

The exponential equation $32 ^ { 2 / 5 } = 4$ can be rewritten in logarithmic form as $\log _ { 32 } 4 = \frac { 2 } { 5 }$, which matches choice B. This follows from the definition of logarithms, where the base of the logarithm is the same as 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.

Change the Exponential Expression to an Equivalent Expression Involving a Logarithm