log2(4x)=log2(4)+log2(x)=2+log2(x);
log2(2x)=log2(2)+log2(x)=1+log2(x)
设t=log2(x),
则y=(2+t)(1+t)
因为1/4 ≤ x ≤ 4,所以-2 ≤ log2(x) ≤ 2,即-2 ≤ t ≤ 2
y=t^2+3t+2=(t+3/2)^2-1/4,- 2 ≤ t ≤ 2,
t=-3/2时,函数取到最小值-1/4,此时x=2^(-3/2)=√2/4.
t=2时,函数取到最大值12,此时x=4.