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A-LevelMathematicsLogarithmic and exponential functions9709/31 · Oct/Nov 2025 · Q25 Marks

Show that the equation log₄(2x + 1) = 2log₄(3x-1)-2 can be written as a quadratic equation in x.

  1. (a)Show that the equation log₄(2x + 1) = 2log₄(3x-1)-2 can be written as a quadratic equation in x.[3]
  2. (b)Hence solve the equation log₄(2x + 1) = 2log₄(3x − 1) − 2.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [B1] State or imply 2 = log4 42
  2. [M1] Use log power, product or quotient law e.g. 2log4 (3x – 1) = log4 (3x – 1)2
  3. [A1] Obtain a correct equation in any form, free of logs
  4. [M1] Solve 3-term quadratic
  5. [A1] Obtain answer 4.59 only

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 3 Variant 1, question 2.

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