Question

Solve the equation log9 (2x−1)=−1
.(1 point)
Responses

x=5
x equals 5

x=0
x equals 0

x=5/9
x equals Start Fraction 5 over 9 End Fraction

x=−4/9

Answer 1

To solve the equation \( \log_9 (2x - 1) = -1 \), we can rewrite it in exponential form.

The equation \( \log_9 (2x - 1) = -1 \) means that:

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

Calculating \( 9^{-1} \):

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

Now, we can set up the equation:

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

Next, add 1 to both sides:

\[
2x = \frac{1}{9} + 1
\]

To combine these terms, express 1 as \(\frac{9}{9}\):

\[
2x = \frac{1}{9} + \frac{9}{9} = \frac{10}{9}
\]

Now, divide both sides by 2:

\[
x = \frac{10}{9} \cdot \frac{1}{2} = \frac{10}{18} = \frac{5}{9}
\]

Thus, the solution to the equation \( \log_9 (2x - 1) = -1 \) is:

\[
x = \frac{5}{9}
\]

Therefore, the correct response is:

**x = 5/9**