Logbase3 (x-2) + log3 (x+6) = 2

log₃ (x - 2) + log₃ (x + 6) = 2

log₃ ((x - 2) (x + 6)) = 2

log₃ (x (x + 6) - 2 (x + 6)) = 2

log₃ (x (x) + x (6) - 2 (x) - 2 (6)) = 2

log₃ (x² + 6x - 2x - 12) = 2

log₃ (x² + 4x - 12) = 2

3² = x² + 4x - 12

9 = x² + 4x - 12

- 9 - 9

0 = x² + 4x - 21

0 = x² + 7x - 3x - 21

0 = x (x) + x (7) - 3 (x) - 3 (7)

0 = x (x + 7) - 3 (x + 7)

0 = (x - 3) (x + 7)

0 = x - 3 or 0 = x + 7

+ 3 + 3 - 7 - 7

3 = x or - 7 = x