Question

Write log9 (-x-9) = -2 in exponential form

9 times out of-2 = -x -9
-2^9 =-x - 9
9^-x-9 = -2
9^-2 =0.0123-x - 9

Answer 1

To rewrite the logarithmic equation \( \log_9 (-x-9) = -2 \) in exponential form, we can follow the definition of logarithms. The equation \( \log_b (y) = x \) can be expressed in exponential form as \( b^x = y \).

For the equation you provided:

\[
\log_9 (-x-9) = -2
\]

We convert it to exponential form:

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

Now, we need to calculate \( 9^{-2} \):

\[
9^{-2} = \frac{1}{9^2} = \frac{1}{81}
\]

Thus, we have:

\[
\frac{1}{81} = -x - 9
\]

From here, you can solve for \( x \) by isolating it:

1. Add \( 9 \) to both sides:

\[
-x = \frac{1}{81} + 9
\]

2. Convert \( 9 \) to a fraction with a denominator of \( 81 \):

\[
9 = \frac{729}{81}
\]

3. Now combine the fractions:

\[
-x = \frac{1 + 729}{81} = \frac{730}{81}
\]

4. Finally, multiply both sides by -1 to solve for \( x \):

\[
x = -\frac{730}{81}
\]

Hence, the value of \( x \) is:

\[
x = -\frac{730}{81}
\]

This concludes the conversion to exponential form and solving for \( x \).