已知集合A={x|3≤3x≤27},B={x|log2x<1}
(1)分别求A∩B,A∪B
(2)已知集合C={x|1<x<a},若C⊆A,求实数a的取值范围.
解:(1)由3≤3x≤27,即3≤3x≤33,∴1≤x≤3,∴A=1,3.
由log2x<1,可得0<x<2,∴B=(0,2).
∴A∩B=1,2).
A∪B=(0,3.
(2)由C⊆A,
当C为空集时,a≤1.
当C为非空集合时,可得 1<a≤3.
综上所述:a的取值范围是a≤3.
根据短文内容,选择正确答案。
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