1)ОДЗ
(3x+1)/(x-2)>0
x=-1/3 U x=2
+ _ +
-----------(-1/3)-------------(2)-------------------
x<-1/3 U x>2
(3x+1)/(x-2)≤2/5
(15x+5-2x+4)/5(x-2)≤0
(13x+9)/(x-2)≤0
x=-9/13 U x=2
+ _ +
-----------[-9/13]-------------(2)-------------------
-9/13≤x<2<br>x∈[-9/13;-1/3)
2)ОДЗ x>0
прологарифмируем по основанию 2
(3log(2)x+1)*log(2)x≤log(2)16
3log²(2)x+log(2)x≤4
log(2)x=a
3a²+a-4≤0
D=1+48=49
a1=(-1-7)/6=-4/3
a2=(-1+7)/6=1
-4/3≤a≤1
-4/3≤log(2)x≤1
x∈[1/2∛2;2]