Решить уравнение: log6 (2x-1) + log6 (x) = log2 (2)

1) 2

2) - 3/2

3) 8

4) {2; -3/2}

Log6 (2x-1) + log6 (x) = 1

log6 (2x-1) + log6 (x) - 1 = 0

log6 (2x-1) + log6 (x) - log6 (6) = 0

log6 (2x-1) * (x) / 6 = 0

х (2 х-1) / 6 = 1

х (2 х-1) / 6 - 1 = 0

х (2 х-1) / 6 - 6/6 = 0

(х (2 х-1) - 6) / 6 = 0

х (2 х-1) - 6 = 0

2 х^2 - х - 6 = 0

D = 1^2 + 4*2*6 = 49

х1 = (1+7) / 2*2 = 8/4 = 2

х2 = (1-7) / 2*2 = - 6/4 = - 3/2 = - 1,5