Find all positive values of 'a' for which the equation log …

Maths Logarithms, Indices and Surds, Partial Fraction Indices and Surds Numeric Response

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Find all positive values of 'a' for which the equation log (ax) = 2 log (x + 1) has the unique root.

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The correct answer is:

Ans. 0004

Sol. log ax = 2 log (x + 1)

⇒ ax = (x + 1) 2 ⇒ x 2 + (2 –a) x + 1 = 0

Let x 1 and x 2 be roots

x 1 = and

x 2 =

For solution exists a 2 –4a ≥ 0

a ≥ 4, a ≤ 0

For positive values a ≥ 4

For a > 4, x 1 and x 2 are different

For a = 4, x 1 and x 2 are same

Hence a = 4.

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