Question

若0＜x＜y＜1，則下列不等式成立的是（　　）

A．( 1 2 )x＜( 1 2 )y	B．x- 1 3 ＜y- 1 3
C．log2x 1 2 ＜log2y 1 2	D．log 1 2 x3＜log 1 2 y3

Answer 1

∵y=( 

1

2

) x是單調(diào)遞減函數(shù)且x＜y∴(

1

2

)x＞(

1

2

)y排除A
∵y=x-

1

3

在x＞0時(shí)單調(diào)遞減且0＜x＜y∴x-

1

3

＞y-

1

3

排除B．
y=log₂x單調(diào)遞增且0＜x＜y∴l(xiāng)og₂x＜log₂y∴

1

2

log2x＜

1

2

log2y∴log2x

1

2

＜log2y

1

2

故C對(duì)．
故選C．