To solve the equation, we can start by simplifying the expression:
log₃(x²) - log₃(x - 1) = 2
log₃(x²/x - 1) = 2
Now, we can rewrite the equation in exponential form:
x²/x - 1 = 3²
x² - x - 3 = 0
We can factor the quadratic equation:
(x - 3)(x + 1) = 0
Setting each factor to zero, we get:
x - 3 = 0 or x + 1 = 0
Solving for x, we find two solutions:
x = 3 or x = -1
Therefore, the solutions to the equation x: log₃(x²) - log₃(x - 1) = 2 are x = 3 and x = -1.
