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A-LevelMathematicsLogarithmic and exponential functions9709/33 · May/June 2017 · Q34 Marks

Using the substitution u = eˣ, solve the equation 4e⁻ˣ = 3eˣ + 4. Give your answer correct to 3 significant figures.

  1. (a)Using the substitution u = eˣ, solve the equation 4e⁻ˣ = 3eˣ + 4. Give your answer correct to 3 significant figures.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [B1] Rearrange as 3u² + 4u – 4 = 0, or 3e²ˣ + 4eˣ – 4 = 0, or equivalent
  2. [M1] Solve a 3-term quadratic for eˣ or for u
  3. [A1] Obtain eˣ = 2/3 or u = 2/3
  4. [A1] Obtain answer x = -0.405 and no other

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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 2017 Paper 3 Variant 3, question 3.

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