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

Question

log
9
⁡
(
−
𝑥
−
9
)
=
−
2
rewritten in exponential form?(1 point)
Responses

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

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

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

−29=−x−9

Answer 1

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

Here, the base \( b \) is \( 9 \), the argument \( a \) is \( -x - 9 \), and \( c \) is \( -2 \).

Using the definition of logarithms, we can rewrite the equation as:

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

So the correct exponential form of \( \log_9(-x - 9) = -2 \) is:

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

Therefore, the correct response is:

9 superscript negative 2 baseline equals negative x minus 9.