Question

对数不等式

不等式log1/2 (3+x)/(3-x)>=log1/2(2x)的解集为 (都是以1/2为底的)

Answer 1

0<1/2<1
所以log1/2(x)是减函数
(3+x)/(3-x)<=2x
真数大于0
0<(3+x)/(3-x)<=2x

0<(3+x)/(3-x)
即(x+3)(x-3)<0
-3<x<3

(3+x)/(3-x)<=2x
(3+x)/(3-x)-2x<=0
(3+x-6x+2x²)/(3-x)<=0
(2x²-5x+3)/(x-3)>=0
即(2x-3)(x-1)(x-3)>=0
零点1,3/2,3
1<=x<=3/2,x>=3
分母不等于0
1<=x<=3/2,x>3

综上
1<=x<=3/2

Answer 2

(3+x)/(3-x)=(2x)解X

Answer 3

(3+x)/(3-x)<=2x
1)3-x>0
3+x<=2x(3-x)
2x^2-5x+3<=0
1<=x<=3/2
2)3-x<0
3+x>=2x(3-x)
2x^2-5x+3>=0
x<=1 or x>=3/2