Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find the number of integers which do not satisfy the inequality log 1/2 (x + 5) 2 > log 1/2 (3x – 1) 2 .
Text Solution
Verified by ExpertsThe correct answer is:
6
(6)
Sol. log 1/2 (x + 5) 2 > log 1/2 (3x – 1) 2
(x + 5) 2 > 0 ⇒ x ∈ R – {– 5} ........(i)
(3x – 1) 2 > 0 ⇒ x ∈ R – 
........(ii)
(x + 5) 2 < (3x – 1) 2
⇒ 8x 2 – 16 x – 24 > 0
⇒ x 2 – 2x – 3 > 0
⇒ (x – 3) (x + 1) > 0
⇒ x ∈ (– ∞ , – 1) ∪ (3, ∞ ) ........(iii)
(i) ∩ (ii) ∩ (iii) gives
(– ∞ , –5) ∪ (–5, –1) ∪ (3, ∞ )
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