(log²(2)x-3log(2)x)²-22(log²(2)x-3log(2)x)+72<0 log²(2)x-3log(2)x=a a²-22a+72<0 a1+a2=22 U a1*a2=72 a1=4 U a2=18 4<a<18 {log²(2)x-3log(2)x>4 (1) {log²(2)x-3log(2)x<18 (2) (1) log(2)x=n n²-3n-4>0 n1+n2=3 U n1*n2=-4 n1=-1 U n2=4 n<-1 U n>4 (2) n²-3n<18 n²-3n-18<0 n1+n2=3 U n1*n2=-18 n1=-3 U n2=6 -3<n<6 -3<n<-1⇒-3<log(2)x<-1⇒1/8<x<1/2 4<n<6⇒4<log(2)x<6⇒16<x<64 Ответ x∈(1/8;1/2) U (16;64)