log3x+ log3(x-2) = 1

Question

This is the correct equation.

log₃x+ log₃(x-2) = 1

Thanks for the help!!

Answer 1

log₃x+ log₃(x-2) = 1

log₃ (x(x-2)) = 1

log₃(x² -2x) = 1

taking 3 as base to both sides

3 ^log₃^{(x2 -2x)} = 3¹

x² -2x = 3

x² -2x - 3 = 0

(x-3)(x+1) =0

x=3 ,x=-1

log of -ve number is invalid

so x= 3