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Question

The complete solution set of the inequality 11+lnx+11lnx>2 is

A
(1e,1)
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B
(1,e)
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C
(1e,e)
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D
(1e,1)(1,e)
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Solution

The correct option is D (1e,1)(1,e)
11+lnx+11lnx>2
The above ineuality is defined when
(i) x>0
(ii) lnx±1x1e,e

Now, 21(lnx)2>2
21(lnx)22>0
22+2(lnx)21(lnx)2>0
2(lnx)21(lnx)2>0
1(lnx)2>0[2(lnx)2>0 x>0 and x1]
(lnx)21<0
lnx(1,1)
x(1e,e)
x(1e,1)(1,e) (x1)

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