Solve for x, they do not have the same base

Question

log₃ x+ 2 log₉ (x-2) = 1

Answer 1

log₃ x + 2 log₉ (x - 2) = 1

2 log₉ x + 2 log₉ (x - 2) = 1

log₉ x² + log₉ (x - 2)² = 1

log₉ [x²(x - 2)²] = 1

9 = x²(x² - 4x + 4)

9 = x⁴ - 4x³ - 4x² - 9

The four solutions are irrational. Please check the data.