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A-LevelMathematicsLogarithmic and exponential functions9709/31 · May/June 2019 · Q24 Marks

Showing all necessary working, solve the equation ln(2x – 3) = 2lnx – ln(x – 1). Give your answer correct to 2 decimal places.

  1. Showing all necessary working, solve the equation ln(2x – 3) = 2lnx – ln(x – 1). Give your answer correct to 2 decimal places.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [M1] Use law for the logarithm of a product, quotient or power
  2. [A1] Obtain a correct equation free of logarithms e.g. (2x-3)(x-1) = x² or x² – 5x + 3 = 0
  3. [M1] Solve a 3-term quadratic obtaining at least one root
  4. [A1] Obtain answer x = 4.30 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 2019 Paper 3 Variant 1, question 2.

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