log4 (x-2) - log4 (x+1) = 1

Answer 1

log₄(x-2)(x+1) = 1
(x-2)(x+1) = 4
x^2 - x - 6 = 0
(x-3)(x+2)
x = 3 or -2
however, x = -2 does not fit the original equation, since log of negative numbers are not defined.

So, the only solution is x=3