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Question

If log0.04(x1)log0.2(x1), then

A
x(1,)
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B
x(,1][2,)
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C
x[2,)
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D
x[1,2]
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Solution

The correct option is C x[2,)
For the inequality to be defined,
x1>0x>1

Now, log0.04(x1)log0.2(x1)
log0.22(x1)log0.2(x1)12log0.2(x1)log0.2(x1)log0.2(x1)2log0.2(x1)log0.2(x1)0
(x1)1 [logax is decreasing for 0<a<1]x2

Hence, x2

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