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The problem asks to solve the logarithmic equation:

\[
\log_3(x - 1) = 2
\]

To solve this equation, follow these steps:

1. **Rewrite the equation in exponential form**: 
   \[
   x - 1 = 3^2
   \]

2. **Simplify**:
   \[
   x - 1 = 9
   \]

3. **Solve for \( x \)**:
   \[
   x = 9 + 1 = 10
   \]

### Solution:
\[
x = 10
\]

Would you like further explanation, or do you have any other questions?

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### Related Questions

1. How would the solution change if the base was different, for example, \( \log_2(x - 1) = 2 \)?
2. How do you solve a logarithmic equation with two logarithmic terms, like \( \log_3(x) + \log_3(x - 1) = 2 \)?
3. What is the domain of the function \( \log_3(x - 1) \)?
4. How would you solve an equation like \( \log_3(x - 1) = \log_3(2x) \)?
5. How can you check if a solution to a logarithmic equation is valid?

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### Tip:
Remember, to convert from logarithmic to exponential form, \( \log_b(a) = c \) translates to \( b^c = a \). This is essential when solving logarithmic equations.

Solve the logarithmic equation log_3(x - 1) = 2.

Learn how to solve the logarithmic equation log_3(x - 1) = 2 with step-by-step instructions. This problem covers logarithmic concepts and converting logarithmic to exponential form, suitable for high school students in Grades 10-12.

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