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Question

The solution set of the inequality (3x4x)ln(x+2)x23x40 is

A
(,0](4,)
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B
(2,0](4,)
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C
(1,0](4,)
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D
(2,1)(1,0](4,)
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Solution

The correct option is D (2,1)(1,0](4,)
(3x4x)ln(x+2)x23x404x((34)x1)ln(x+2)(x4)(x+1)0

For log to be defined,
x+2>0x>2 (1)

The critical points are x=1,0,4


Hence, by wavy curve method,
x(2,1)(1,0](4,)

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