Question

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

Answer 1

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

Applying this to your equation, we have:

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

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

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

So, we can rewrite the equation as:

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

Now, if you want to isolate \( x \), you can add 9 to both sides:

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

Converting 9 to a fraction with a common denominator:

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

Now combine the fractions:

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

Finally, multiply both sides by -1:

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

So, the exponential form of the original logarithmic equation is:

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