The sum of the roots of the equation x + 1 − 2 log 2 (3 + 2…

Maths Logarithms, Indices and Surds, Partial Fraction JEE Mains 2021 Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

The sum of the roots of the equation x + 1 − 2 log 2 (3 + 2 x ) + 2 log 4 (10 − 2 − x ) = 0, is :

log 2 14

log 2 11

log 2 12

log 2 13

Text Solution

Verified by Experts

The correct answer is:

x + 1 − 2 log 2 (3 + 2 x ) + 2 log 4 (10 − 2 − x ) = 0

log2(2 x+1 ) − log 2 (3 + 2 x ) 2 + log 2 (10 − 2 − x ) = 0

⇒ 20.2 x − 2 = 9 + 2 2x + 6.2 x

∴ (2 x ) 2 − 14 (2 x ) + 11 = 0

Roots are

x 1 + x 2 = log 2 (11)

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