1
ОДЗ
x+1>0⇒x>-1
2x+1>0⇒x>-0,5
x∈(-0,5;∞)
log(6)(x+1)(2x+1)<1<br>2x²+x+2x+1<6<br>2x²+3x-5<0<br>D=9+40=49
x1=(-3-7)/4=-2,5
x2=(-3+7)/4=1
-2,5x∈(-0,5;1)
2
ОДЗ
(x-2)/(1-x)>0
x=2 U x=1
1log(3)[(x-2)/(1-x)]>0
(x-2)/(1-x)>1
(x-2-1+x)/(1-x)>0
(2x-3)/(1-x)>0 x=1,5 U x=1
1x∈(1;1,5)
log(3)[(x-2)/(1-x)]<2<br>(x-2)/(1-x)<9<br>(x-2-9+9x)/(1-x)<0<br>(10x-11)/(1-x)<0<br>x=1,1 x=1
x<1 U x>1,1
x∈(1,1;1,5)
3
x>0
(1+lgx)²-lgx-3≥0
lg²x+2lgx+1-lgx-3≥0
lg²x+lgx-2≥0
lgx=a
a²+a-2≥0
a1+a2=-1 U a1*a2=-2
a1=-2 U a2=1
a≤-2≥lgx≤-2⇒x≤0,01
a≥1⇒lgx≥1⇒x≥10
x∈(0;0,01] U [10;∞)