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A-LevelMathematicsLogarithmic and exponential functions9709/23 · May/June 2021 · Q15 Marks

Solve the equation In(2 + x) – lnx = 2 ln 3.

  1. (a)Solve the equation In(2 + x) – lnx = 2 ln 3.[3]
  2. (b)Hence solve the equation In(2 + cot y) – In(cot y) = 2 ln 3 for 0 < y < π. Give your answer correct to 4 significant figures.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [M1] Use at least one relevant logarithm property correctly
  2. [A1] Obtain correct equation (2+x)/x = 9 or equivalent with no logarithms
  3. [A1] Obtain x = 1/4
  4. [M1] Attempt value of y from tan y = 1÷(their (a))
  5. [A1] Obtain 1.326

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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, May/June 2021 Paper 2 Variant 3, question 1.

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