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A-LevelMathematicsLogarithmic and exponential functions9709/21 · Oct/Nov 2022 · Q24 Marks

Use logarithms to solve the equation 14e⁻²ˣ = 5ˣ⁺¹, giving your answer correct to 3 significant figures.

  1. Use logarithms to solve the equation 14e⁻²ˣ = 5ˣ⁺¹, giving your answer correct to 3 significant figures.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [*M1] Apply logarithms correctly to both sides and apply power law at least once
  2. [A1] Obtain ln14-2x = (x+1)ln5 (OE with x no longer part of a power.)
  3. [DM1] Attempt solution of linear equation (Must have ln14-ln5=x(2+ln5).)
  4. [A1] Obtain 0.285

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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, Oct/Nov 2022 Paper 2 Variant 1, question 2.

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