Solve the following inequalities
`(i) |log_(3)x|-log_(3)x-3 lt 0` `(ii)(x-1)/(log_(3)(9-3^(x))-3) le 1`
`(iii)log_((x-1)/(x-5))(x-2) gt 0` `(iv) log_(x)(x^(3)-x^(2)-2x) lt 3`

Answer

`(i) ((1)/(3^(3//2)),oo)` `(ii) [log_(3)9//10,2)` `(iii) (5,oo)` `(iv) (2,oo)`