Equations And Inequalities Question 25
Question: Solution set of the inequality $ \frac{1}{2^{x}-1}>\frac{1}{1-{2^{x-1}}} $ is
Options:
A) $ (1,\infty ) $
B) $ (0,log_2(4/3)) $
C) $ (-1,\infty ) $
D) $ (0,log_2(4/3))\cup (1,\infty ) $
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] Put $ 2^{x}=t. $ Then $ t>0. $ Now, given inequality becomes $ \frac{1}{t-1}>\frac{2}{2-t}\Rightarrow \frac{1}{t-1}-\frac{2}{2-t}>0\Rightarrow \frac{2-t-2t+2}{(t-1)(2-t)}>0 $ From sign scheme we get $ 1<t<4/3ort>2. $
$ \Rightarrow 1<2^{x}<4/3 $ or $ 2^{x}>2 $
$ \Rightarrow x\in (0,log_2(4/3))\cup (1,\infty ) $
BETA
