1.

Solution of inequality `log_(sin x)(log_(3)(log_(0.2)x))lt0` isA. `[0, 2]`B. `(0, (1)/(2))`C. `((1)/(125), (1)/(2))`D. `(0, (1)/(125))`

Answer» Correct Answer - 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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