Which of the following equations is log9(−x−9)=−2

Question

rewritten in exponential form?(1 point)
Responses

−29=−x−9
negative 2 superscript 9 baseline equals negative x minus 9

9⋅−2=−x−9
9 times negative 2 equals negative x minus 9

9−2=−x−9
9 superscript negative 2 baseline equals negative x minus 9

9−x−9=−2

Answer 1

To rewrite the equation \( \log_9(-x - 9) = -2 \) in exponential form, we use the definition of logarithms. The equation \( \log_b(a) = c \) is equivalent to \( b^c = a \).

In this case:

• \( b = 9 \)
• \( c = -2 \)
• \( a = -x - 9 \)

Using the logarithmic definition, we rewrite the equation as:

\[ 9^{-2} = -x - 9 \]

From the response choices given, the correct choice is:

9 superscript negative 2 baseline equals negative x minus 9 (9^{-2} = -x - 9).