Log 0.6 (x+2) + log0.6 (6-x) = log 0.6 (x+8)

Log 0.6 (x+2) + log0.6 (6-x) = log 0.6 (x+8)

log0.6 ((x+2) (6-x)) = log0.6 (x+8)

(x+2) (6-x) = x+8

6x-x²+12-2x=x+8

-x²+3x+4=0

x²-3x-4=0

D=9+16=25 (2 к)

x1 = (3+5) / 2=4

x2 = (3-5) / 2=-1

Проверка:

1) log0.6 ((4+2) (6-4)) = log0.6 (4+8)

log0.6 (12) = log0.6 (12)

x=4 - корень уравнения

2) log0.6 ((-1+2) (6+1)) = log0.6 (-1+8)

log0.6 (7) = log0.6 (7)

x=-1 - корень уравнения

Ответ: - 1; 4