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?

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?

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.