Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Find all real numbers x which satisfy the equation
2 log 2 log 2 x + log 1/2 log 2 
= 1.
Text Solution
Verified by ExpertsThe correct answer is:
2
x = 8
Sol. 2 log 2 log 2 x + log 1/2 log 2 
= 1 ⇒ log 2 (log 2 x) 2 –log 2 log 2 
=1
⇒ log 2 
= 1 ⇒ 
= 2
let log 2 x = y
∴ y 2 – 2y – 3 = 0 ⇒ (y – 3) (y + 1) = 0
∴ y = 3, –1 ⇒ log 2 x = 3, –1,
but log 2 x > 0
∴ log 2 x = – 1 is not possible
⇒ x = 8
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