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

Question

rewritten in exponential form?(1 point)
Responses

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

−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

Answer 1

To rewrite the logarithmic equation \( \log_9(-x - 9) = -2 \) in exponential form, we use the definition of logarithms, which states that if \( \log_b(a) = c \), then it can be rewritten as \( b^c = a \).

In this case:

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

Using the definition, we can write:

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

Now, simplify \( 9^{-2} \):

\[ \frac{1}{9^2} = -x - 9 \]

This gives us the correct exponential form of the original logarithmic equation.

Looking at your options, the corresponding exponential form \( 9^{-2} = -x - 9 \) matches with:

9^{-2} = -x - 9.

So the answer is:

9^{-2} = -x - 9