已知正数x,y满足2x-y≤0,x-3y+5≥0,则z=log2x+log2y+1的最大值是?

A. 1 B. 8 C. 4 D. 2
2025-06-21 08:06:19
推荐回答(1个)
回答1:

2x-y≤0,x-3y+5≥0,解得3y-5≤x≤y/2
y/2≥3y-5,解得y≤2,又y>0,因此0z=log2(x)+log2(y)+1
=log2(xy) +1
≤log2[(y/2)y]+1
=log2(y²/2)+1
=2log2(y) -1+1
=2log2(y)
≤2log2(2)=2
选D。