Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If log 0.5 log 5 (x 2 – 4) > log 0.5 1, then ‘x’ lies in the interval
A
(– 3, – 
) ∪ ( 
, 3)
) ∪ ( , 3)
B
(– 3, – 
) ∪ ( 
, 2)
) ∪ ( , 2)
C
( 
, 3 
)
, 3 )
D
φ
Text Solution
Verified by ExpertsThe correct answer is:
A
log 0.5 log 5 (x 2 – 4) > log 0.5 1 ; log 0.5 log 5 (x 2 – 4) > 0
⇒ x 2 – 4 > 0 ⇒ x ∈ (– ∞ , –2) ∪ (2, ∞ ) ....(i)
log 5 (x 2 – 4) > 0 ⇒ x 2 – 5 > 0
⇒ x ∈ (– ∞ , – 
) ∪ ( 
, ∞ ) ....(ii)
log 5 (x 2 – 4) < 1
⇒ x 2 – 9 < 0 ⇒ x ∈ (–3, 3) ....(iii)
(i) ∩ (ii) ∩ (iii) ⇒ x ∈ (–3, 
) ∪ ( 
, 3)
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