Question

Set of all the values of x satisfying the inequality

$\log_{x + \frac{1}{x}}\left( \log_{2}\frac{x - 1}{x + 2} \right)$> 0 is

• A. (– 5, – 2)
• B. (2, 5)
• C. (5, ¥)
• D. f

Answer 1

Answer: (D)

f

Answer 2

\ $\frac{x - 1}{x + 2}$> 0; \ x > 1, x < – 2 ….(i)

But x + $\frac{1}{x}$ > 0; \ $\frac{x^{2} + 1}{x} > 0$ ̃ x > 0 ….(ii)

From (i) & (ii) x > 1; $\log_{x + \frac{1}{x}}\left( 1og_{2}\frac{x - 1}{x + 2} \right) > 0$

Take antilog, log₂$\frac{x - 1}{x + 2}$>1

Take antilog$\frac{x - 1}{x + 2}$ > 2; $\frac{x + 5}{x + 2}$ < 0 ̃ xÎ(–5_, –2)

But not true as x > 1