Question

The solution set of the inequality

$\log_{(\cos x)^{2}}{}$ (3 – 2x) <$\log_{(\cos x)^{2}}{}$ (2x – 1) is –

• A. $\left( \frac{1}{2},1 \right)$
• B. (– ¥, 1)
• C. $\left( \frac{1}{2},3 \right)$
• D. (1, ¥) – $\sqrt{2n\pi}$"nÎN

Answer 1

Answer: (A)

$\left( \frac{1}{2},1 \right)$

Answer 2

\ 3 – 2x > 0 & 2x – 1> 0 for log to exist

x < 3/2 & x > 1/2 \ x Î $\left( \frac{1}{2},\frac{3}{2} \right)$ ...(1)

Now 0 < cos²x < 1

Take antilog

3 – 2x > 2x – 1 ̃ 4x < 1 ̃ x < 1 ...(2)

From (1) & (2) x Î$\left( \frac{1}{2},1 \right)$