Which of the following is the equation log subscript x baseline 4 equals negative 2 written in exponential form?

Question

(1 point)
Responses

left parenthesis 4 right parenthesis superscript negative 2 baseline equals x
Image with alt text: left parenthesis 4 right parenthesis superscript negative 2 baseline equals x

x superscript negative 2 baseline equals 4
Image with alt text: x superscript negative 2 baseline equals 4

2 superscript negative 2 baseline equals x
Image with alt text: 2 superscript negative 2 baseline equals x

4 superscript x baseline equals negative 2
Image with alt text: 4 superscript x baseline equals negative 2

Answer 1

The equation \( \log_x 4 = -2 \) can be rewritten in exponential form. The logarithmic equation states that \( x^{-2} = 4 \).

Rearranging this gives us:

\[ 4 = x^{-2} \quad \text{or} \quad (4)^{(-2)} = x \]

Therefore, the correct answer from the given options is:

\[ (4)^{-2} = x \]

So the correct response is:

left parenthesis 4 right parenthesis superscript negative 2 baseline equals x