Question

Solve for log9 (2x-1) = -1

x = 5/9
X = 0
X = -4/9
X = 5

Answer 1

To solve the equation \( \log_9 (2x - 1) = -1 \), we'll start by using the definition of a logarithm.

The equation can be rewritten in exponential form:

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

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

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

Now substitute this back into the equation:

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

Next, we'll solve for \( x \). Begin by adding 1 to both sides:

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

Convert 1 to a fraction with a denominator of 9:

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

So we have:

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

Now, divide both sides by 2:

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

Thus, the solution for \( x \) is:

\[
\boxed{\frac{5}{9}}
\]