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

(log₁/₆ x)²>4, (log₁/₆x)²-4>0, (log₁/₆x+2)*(log₁/₆x-2)>01. log₁/₆x<-2, -2=log₁/₆(1/6)⁻²=log₁/₆6²=log₁/₆ 36log₁/₆ x<log₁/₆ 36,   основание 0<1/6<1, знак меняем{x>0x>36, => x>362. log₁/₆ x>2,  2=log₁/₆ (1/6)²=log₁/₆ (1/36)log₁/₆ x>log₁/₆ (1/36){x>0x<1/36ответ: х∈(0; 1/36)U(36;∞)