Question

Solution of the inequality |3 - ${\log }_{2}x$| < 2 contains the interval.

• A. x ∈ (2, 32)
• B. x > 2
• C. x ∈ [2, 32]
• D. x < 32

Answer 1

The correct option is A

x ∈ (2, 32)

|3 - ${\log }_{2}x$| < 2 - - - - - - (I)

By definition of logarithm x > 0

Since, |3 - ${\log }_{2}x$| < 2

$\Rightarrow$ 3 - ${\log }_{2}x$ < 2 or 3 - ${\log }_{2}x$ > -2

Common part of equation II and equation III is x ∈ (2, 32)

Correct option a.