`Sol v e(log)_x(x^2-1)lt=0.`

Answer

` x in (1, sqrt2)`

Explanation

Given ` log_(x)(x^(2)-1) le 0`
If ` x gt 1`
`rArr 0 lt x^(2) - 1 le 1`
` rArr 1 lt x^(2) le 2`
` rArr x in [-sqrt2, -1) uu (1, sqrt2]`
` rArr x in (1, sqrt2]`
If ` 0 lt x lt 1`
` rArr x^(2) - 1 ge 1`
`rArr x^(2) ge 2`
`rArr x in ( - infty, -sqrt2]uu[sqrt2, infty)`
` rArr x = phi`
Thus,`x in (1, sqrt2]`