若 根号2≤x≤8,求函数y=(log2二分之x)(log4四分之x)最大值 真心急！明天要用 好心人拜托了！

若 根号2≤x≤8,求函数y=(log2二分之x)(log4四分之x)最大值 真心急！明天要用 好心人拜托了！

y=(log2二分之x)(log4四分之x)
=(log2(x)-1)(log4(x)-1)
=(log2(x)-1)((1/2)log2(x)-1)
=(1/2)(log2(x))^2-(3/2)log2(x)+1
=(1/2)[log2(x)-(3/2)]^2-(1/8)

而：根号2<=x<=8
所以：1/2<=log2(x)<=3
-1<=log2(x)-(3/2)<=3/2
0<=[log2(x)-(3/2)]^2<=9/4
所以，-1/8<=(1/2)[log2(x)-(3/2)]^2-(1/8)<=1
即：-1/8<=y<=1

y=(log2二分之x)(log4四分之x) 根号2≤x≤8,
y=(logx-0.301)(logx-0.602)
y=（logx0^2-0.903logx+0.1812 y=logx(logx-0.903)+0.1812
当x=8时 y=0.1812为最大