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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Feb/Mar 2020 · Q24 Marks

Solve the equation In 3 + ln(2x + 5) = 2ln(x + 2). Give your answer in a simplified exact form.

  1. Solve the equation In 3 + ln(2x + 5) = 2ln(x + 2). Give your answer in a simplified exact form.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

  1. [M1] Use law of logarithm of a power and sum and remove logarithms
  2. [A1] Obtain a correct equation in any form, e.g. 3(2x+5)=(x+2)²
  3. [M1] Use correct method to solve a 3-term quadratic, obtaining at least one root
  4. [A1] Obtain final answer x = 1+2√3 or 1 + √12 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, Feb/Mar 2020 Paper 3 Variant 2, question 2.

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