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Solve (0.5)^(log(3)log((1//5)))(x^(2)-4/...

Solve `(0.5)^(log_(3)log_((1//5)))(x^(2)-4/5)gt 1`.

Text Solution

Verified by Experts

The correct Answer is:
`x in(-3/sqrt5, - 1)cup(1, 3/sqrt5)`
`(0.5)^(log_(3) log_((1//5))(x^(2)-4/5)) gt 1`
`rArr (1/2)^(log_(3)log_(1//5)(x^(2)-4/5))gt(1/2)^(0)`
` rArr log_(3) log_(1//5)(x^(2)-4/5)lt0`
` rArr 0 lt log_(1//5)(x^(2)-4/5) lt 1`
` rArr 1 gt x^(2) - 4/5 gt 1/5`
` rArr 1 lt x^(2) lt9/5`
` rArr x in(-3/sqrt5,-1)uu(1,3/sqrt5)`
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