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Solution of inequality log(sin x)(log(3)...

Solution of inequality `log_(sin x)(log_(3)(log_(0.2)x))lt0` is

A

`[0, 2]`

B

`(0, (1)/(2))`

C

`((1)/(125), (1)/(2))`

D

`(0, (1)/(125))`

Text Solution

Verified by Experts

The correct Answer is:
D
Solution of inequality ………
`log_(sin x)(log_(3)(log_(0.2)x))lt0 = log_(sin x)1`
`log_(3)(log_(0.2)x)gt1`
`implies log_(0.2)x gt 3 = log_(0.2) (0.2)^(3)`
`implies 0 lt x lt (0.2)^(3) implies 0 lt x lt (1)/(125)`
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