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A-LevelMathematicsLogarithmic and exponential functions9709/22 · Feb/Mar 2024 · Q14 Marks

Use logarithms to solve the equation 3⁴ˣ⁺³ = 5²ˣ⁺⁷. Give your answer correct to 3 significant figures.

  1. Use logarithms to solve the equation 3⁴ˣ⁺³ = 5²ˣ⁺⁷. Give your answer correct to 3 significant figures.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.

  1. [M1] Apply logarithms to both sides and apply power law at least once
  2. [A1] Obtain (4x+3)ln3 = (2x+7)ln5
  3. [DM1] Attempt solution of linear equation
  4. [A1] Obtain 6.78 [Or greater accuracy.]

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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 2024 Paper 2 Variant 2, question 1.

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