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Question

Solution set of the inequality
12x1>112x1is


A

(1,)

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B

(0,log2 (4/3))

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C

(1,)

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D

(0,log2 (4/3))(1,)

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Solution

The correct option is D

(0,log2 (4/3))(1,)


Put 2x=t. Then t>0. The given inequality becomes
1t1>22t1t122t>02t2t+2(t1)(2t)>043t(t1)(2t)>0(t1)(t4/3)(t2)>0Using sign chart, we get1<t<4/3 or t>21<2x<4/3 or 2x>20<x<log2 (4/3) or x>1
Thus, solution set is
(0,log2 (4/3))(1,)


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