设y=log2(x),则:y∈[1,3]
f(x)=log2(x/2)·log2(x/4)
=(log2(x)-1)(log2(x)-2)
=(y-1)(y-2)
=y^2-3y+2
=(y-(3/2))^2-(1/4)
当y=3/2,f(x)有最小值-1/4
而:f(2)=0,f(8)=log2(4)=2
所以:f(x)最大值=2
设y=log2(x),则:y∈[1,3]
f(x)=log2(x/2)·log2(x/4)
=(log2(x)-1)(log2(x)-2)
=(y-1)(y-2)
=y^2-3y+2
=(y-(3/2))^2-(1/4)
当y=3/2,f(x)有最小值-1/4
而:f(2)=0,f(8)=log2(4)=2
所以:f(x)最大值=2