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Maths Fundamental of Mathematics Logarithmic Inequalities Subjective Type

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Solve the following inequalities :

(i) 2 <

(ii)log x² (2 + x) < 1

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(i)

3x 2 + 1 > 1 ⇒ x 2 > 0 ⇒ x ∈ R – {0}

2 < (3x 2 + 1) 1/2 ⇒ 3x 2 + 1 > 4 ⇒ (x – 1) (x + 1) > 0

⇒ x ∈ (– ∞ , –1) ∪ (1, ∞ )

(ii) (x + 2) < 1 x + 2 > 0 x > – 2

Case -I : when 0 < x 2 < 1 x ∈ (–1, 0) ∪ (0, 1)

then x + 2 > x 2 ⇒ x 2 – x – 2 < 0

Case -II : x 2 > 1 |x| > 1

x + 2 < x 2 ⇒ x 2 – x – 2 > 0

Hence,

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