Log3(x-2)+log3(x+6)=2
2=log3(9)
log3(x-2)+log3(x+6)=log3(9)
log3(x-2)(x+6)=log3(9)
(x-2)(x+6)=9
x²+6x-2x-12-9=0
x²+4x-21=0
x1+x2= -4
x1x2= -21
x1= -7; x2= 3
Проверка:
log3(x-2)+log3(x+6)=log3(9)
log3(-7-2)+log3(-7+6)=log3(9)
log3(-9)+log3(-1)=log3(9)
log3(9)=log3(9)
2=2
log3(3-2)+log3(3+6)=log3(9)
log3(1)+log3(9)=log3(9)
log3(9)=log3(9)
2=2
Ответ: -7; 3