Question

The set of real values of x for which
`2^("log"_(sqrt(2))(x-1)) gt x+ 5,` is
A. `(-oo, -1) cup (4, oo)`
B. `(4, oo)`
C. `(-1, 4)`
D. none of these

Answer 1

Correct Answer - B
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)`