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log2|x-1|<1...

`log_2|x-1|<1`

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`log_2 |x-1| lt 1`
`=>|x-1| lt 2^1`
`=>|x-1| lt 2`
Case 1: When `x ge1`,
Then, `x -1 lt 2`
`=> x lt 3`
`:. x in [1,3)`
...
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