Solution set of the inequality `1/(2^(x) - 1) gt 1/(1-2^(x-1))` isA. ` (1, infty)`B. ` (0, log_(2) (4//3))`C. ` (-1, infty)`D. ` (0, log_(2)(4//3))cup(1, infty)`

Solution set of the inequality `1/(2^(x) - 1) gt 1/(1-2^(x-1))` isA. `

1.	Solution set of the inequality `1/(2^(x) - 1) gt 1/(1-2^(x-1))` isA. ` (1, infty)`B. ` (0, log_(2) (4//3))`C. ` (-1, infty)`D. ` (0, log_(2)(4//3))cup(1, infty)`
Answer» Correct Answer - D Put ` 2^(x) = t." Then " t gt 0`. The given inequality becomes ` 1/(t-1) gt 2/(2 - t)` ` rArr 1/(t-1) - 2/(2 - t) gt 0` ` rArr (2-t - 2t + 2)/((t-1)(2-t)) gt 0` ` rArr (4 - 3t)/((t-1)(2-t)) gt 0` ` rArr (t-1)(t-4//3)(t-2) gt 0` . From above sign scheme, we get ` 1 lt t 4//3 or t gt 2`. `rArr 1 lt 2^(x) lt 4//3 or 2^(x) gt 2` ` rArr 0 lt x lt log_(2) (4//3) or x gt 1`