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A-LevelMathematicsLogarithmic and exponential functions9709/33 · May/June 2024 · Q14 Marks

Solve the equation 8³⁻⁶ˣ = 4×5⁻²ˣ. Give your answer correct to 3 decimal places.

  1. Solve the equation 8³⁻⁶ˣ = 4×5⁻²ˣ. Give your answer correct to 3 decimal places.[4]

Mark scheme

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

  1. [B1] Use law of the logarithm of product or quotient on each side
  2. [DB1] Use law of logarithm of a power involving x on ONE side, e.g. ln 8³ + (-)6x ln 8 or (3 – 6x) ln 8 or (9-18x) ln2 or ln 4-2xln 5
  3. [B1] Obtain a correct linear equation in x, e.g. (3-6x)ln8 = (9-18x) In2 = ln 4-2x ln 5
  4. [B1] Obtain answer x = 0.524

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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 2024 Paper 3 Variant 3, question 1.

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