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Solve log(10)(x^(2)-2x-2) le 0....

Solve ` log_(10)(x^(2)-2x-2) le 0`.

Text Solution

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The correct Answer is:
`x in [-1, 1-sqrt3) cup(1+sqrt3, 3]`
` log_(10)(x^(2)-2x-2) le 0`
`rArr 0 ltx^(2) - 2x - 2 le 10^(0)`
` rArr x^(2) - 2x - 2 gt 0 and x^(2) - 2x - 3 le 0`
`rArr x lt1 -sqrt3 or x gt 1 + sqrt3`...(i)
` and (x-3)(x+1) le 0`
` rArr x in [-1, 3]` ...(ii)
From(i) and (ii)
`x in [-1, 1-sqrt()3)cup(1+sqrt()3,3]`
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