Question

`(log)_(0. 3)(x-1)<(log)_(0. 09)(x-1)t h e nx` in the lies in the interval- `(2,oo)` b. `(1,2)` c.`(-2,-1)` d. `(-oo,2)`<br>A. `(2, oo)`
B. `-2, -1`
C. `(1, 2)`
D. none of these

Answer 1

Correct Answer - A
We have,
`"log"_(0.3) (x-1) lt "log"_(0.09) (x-1)`
Clearly, it is defined for ` x gt 1`
Now,
`"log"_(0.3)(x-1) lt "log"_(0.09) (x-1)`
`rArr "log"_(0.3)(x-1) lt "log"_((0.3))^(2) (x-1)`
`rArr "log"_(0.3)(x-1) lt (1)/(2) "log"_(0.3) (x-1)`
`rArr "log"_(0.3)(x-1) lt 0 rArr x -1 gt (0.3)^(0) rArr x gt 2 rArr x in (2, oo)`