Question

Решите неравенство.
log^2(основание - 1/6)X > 4

Answer 1

(log₁/₆ x)²>4, (log₁/₆x)²-4>0, (log₁/₆x+2)*(log₁/₆x-2)>0

1. log₁/₆x<-2, -2=log₁/₆(1/6)⁻²=log₁/₆6²=log₁/₆ 36
log₁/₆ x<log₁/₆ 36,   основание 0<1/6<1, знак меняем
{x>0
x>36, => x>36

2. log₁/₆ x>2,  2=log₁/₆ (1/6)²=log₁/₆ (1/36)
log₁/₆ x>log₁/₆ (1/36)
{x>0
x<1/36
ответ: х∈(0; 1/36)U(36;∞)