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B
x∈(0,14]
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C
x∈[4,∞)
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D
x∈(1,2)
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Solution
The correct option is Cx∈[4,∞) √xlog2√x≥2⇒xlog2√x≥4Takinglogbothsideswithbase2,weget⇒(log2√x)(log2x)≥log24⇒12(log2x)(log2x)≥2⇒(log2x)2≥4⇒((log2x)−2]((log2x)+2]≥0⇒log2x≤−2orlog2x≥2⇒x≤2−2orx≥22⇒x≤14orx≥4⇒x∈(0,14]∪[4,∞)