Solution set of the inequality 2 − log 2 (x 2 + 3x) ≥ 0 is :

Maths Fundamental of Mathematics Logarithmic Inequalities Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

[ − 4, 1]

[ − 4, − 3) ∪ (0, 1]

( − ∞, − 3) ∪ (1, ∞ )

( − ∞, − 4) ∪ [1, ∞ )

Text Solution

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The correct answer is:

2 – log 2 (x 2 + 3x) ≥ 0 ⇒ log 2 (x 2 + 3x) ≤ 2

x 2 + 3x > 0 ⇒ x ∈ (– ∞ , – 3) ∪ (0, ∞ ) .....(i)

and x 2 + 3x ≤ 4

⇒ (x –1) (x + 4) ≤ 0 ⇒ x ∈ [–4, 1] .....(ii)

(i) ∩ (ii) ⇒ x ∈ [–4, –3) ∪ (0, 1]

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