设集合A={X|2[(log(1/2)^x]^2-7log2^x+3

Question

设集合A={X|2[(log(1/2)^x]^2-7log2^x+3

Answer 1

2[(log(1/2) x]²-7log2 x+3≤0,--->2(log2 x)²-7log2 x+3≤0,
(2log2 x -1)(log2 x -3)≤0,1/2≤log2 x ≤3,
f(x)=log2 (x/2^a)*log2 (x/4)=[log2 x -a]*[log2 x -2]=(log2 x)²-(a+2)(log2 x)+2a,
令t=log2 x,则右边为g(t)=t²-(a+2)t+2a,1/2≤t≤3,
对称轴t=(a+2)/2,定义域中心为(1/2 +3)/2=7/4,
若(a+2)/2≥7/4即a≥3/2,则最大值为g(1/2)=1/4 -(a+2)/2 +2a=2,解得a=11/6,
若(a+2)/2