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Question

Solution set of the inequality log0.8(log6x2+xx+4)<0


A

(-4,-3)

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B

(3,4)(8,)

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C

(3,)

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D

(4,3)(8,)

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Solution

The correct option is D

(4,3)(8,)


Since, the base of log0.8(log6x2+xx+4)<0
is less than 1,
log6(x2+xx+4)>1x2+xx+4>6x2+xx+46>0
x2+x6x24(x+4)>0(x8)(x+3)(x+4)>0,x4.
4<x<3 or x>8.
Thus, required solution set is (4,3)(8,)


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