Question

Considere x ∈ IR, x > 2. Se x satisfaz a igualdade log(3x − 6) = log 3 − log(x − 2), então x é igual a:
a)3
b)4
c)5
d)6

Answer 1

log(3x − 6) = log 3 − log(x − 2)
log(3x − 6) + log(x − 2) = Log 3
log (3x − 6).(x-2) = log 3
(3x -6).(x-2) = 3
3x²-6x -6x +12 - 3 = 0
3x² -12x +9 = 0 ===> : (3)
x² -4x +3 = 0
∆=16-12=4 => √∆=2
x' = 4+2/2 = 6/2 = 3 ✓
x" = 4-2/2 = 2/2= 1 (não serve)
==> S: {3} ✓