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Question

The set of real values of x for which log0.2x+2x1 is

A
(,52](0,+)
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B
[52,+)
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C
(,2)(0,+)
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D
None of these
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Solution

The correct option is A (,52](0,+)
log0.2x+2x1 ....(i)
For log to be defined, x+2x>0x>0 or
x < -2
Now from(i), log0.2x+2xlog0.20.2
x+2x0.2 .....(ii)
Case (i) x > 0
From (ii),x+20.2x
0.8x2
x52.
Case (ii) x < -2
From(ii), x+20.2x0.8x2x52
xϵ(,52](0,).

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