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Question

The inequality xlog2 x2 is satisfied by

A
only one value of x
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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 options are
B x(0, 14]
C x[4, )
xlog2 x2xlog2 x4Taking log both sides with base 2, we get(log2 x)(log2 x)log2 412(log2 x)(log2 x)2(log2 x)24((log2 x)2]((log2 x)+2]0log2 x2 or log2 x2x22 or x22x14 or x4x(0, 14][4, )

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