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A-LevelMathematicsLogarithmic and exponential functions9709/31 · May/June 2024 · Q24 Marks

Solve the equation ln(x-5) = 7-lnx. Give your answer correct to 2 decimal places.

  1. Solve the equation ln(x-5) = 7-lnx. Give your answer correct to 2 decimal places.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [M1] Use law of logarithm of a product (or quotient) on correct terms
  2. [DM1] Use correct method to eliminate logarithm
  3. [A1] Obtain a correct quadratic in x, e.g. x² −5x-e⁷ =0 (allow decimals)
  4. [A1] Obtain answer x = 35.71 only

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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 2024 Paper 3 Variant 1, question 2.

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