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The set of all x for which log(1+ x) le ...

The set of all x for which `log(1+ x) le x` is equal to …… .

A

`(-oo, -1) cup (4, oo)`

B

`(4, oo)`

C

`(-1, 4)`

D

none of these

Text Solution

Verified by Experts

We have ,
`2^("log"_(sqrt(2))(x-1)) gt x+ 5`
`rArr 2^(2"log"2 (x-1)) gt x+ 5`
`rArr (x-1)^(2) gt x+ 5`
`rArr x^(2) -3x-4 gt 0`
`rArr (x-4)(x+1) gt 0`
`rArr x lt -1 "or" x gt 4`
`rArr x gt 4 " " [because "log"_(sqrt(2))(x-1) " is defined for " (x-1) gt 0]`
`rArr x in (4, oo)`
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