y =log1/2(x/4)*log1/4(x/2),x属于【2,4】,求最大值

y =log1/2(x/4)*log1/4(x/2),x属于【2,4】,求最大值
y =log1/2(x/4)*log1/4(x/2),x属于【2,4】,求最大值

y =log1/2(x/4)*log1/4(x/2),x属于【2,4】,求最大值
y =log1/2(x/4)*log1/4(x/2) 化简得：
y=log1/2（(1/2)*(1/2)*x）*（1/2）*log1/2（（1/2）*x）
=1/2*（2+log1/2（x））*（1+log1/2（x））
令log1/2（x）=t∈[log1/2(4),log1/2(2)]=[-2,-1]
∴y=1/2(t+2)(t+1)
=1/2(t^2+3t+2)
=1/2((t+3/2)^2-1/4)
∵t∈[-2,-1]
∴t+3/2∈[-1/2,1/2]
(t+3/2)^2∈[0,1/4]
1/2((t+3/2)^2-1/4)∈[-1/8,0]
∴y∈[-1/8,0]
∴y最大值为0