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A-LevelMathematicsLogarithmic and exponential functions9709/33 · May/June 2025 · Q24 Marks

Solve the equation 2 ln (2x+3) - ln(2x + 5) = ln(3x).

  1. Solve the equation 2 ln (2x+3) - ln(2x + 5) = ln(3x).[4]

Mark scheme

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

  1. [M1*] Use the correct rule for logarithm of a power, product or quotient or an equivalent method using exponentials.
  2. [A1] Obtain an equation free of logarithms. E.g. (2x+3)²/(2x+5) = 3x.
  3. [DM1] Form a 3-term quadratic from completely correct use of logarithms and solve for x. 2x²+3x-9=0.
  4. [A1] State final answer only. Rejection of negative value if given must be clear.

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, May/June 2025 Paper 3 Variant 3, question 2.

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