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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Oct/Nov 2022 · Q14 Marks

Solve the equation 2^(3x−1) = 5(3^(1−x)). Give your answer in the form (ln a)/(ln b) where a and b are integers.

  1. Solve the equation 2^(3x−1) = 5(3^(1−x)). Give your answer in the form (ln a)/(ln b) where a and b are integers.[4]

Mark scheme

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

  1. [M1] Use law of the logarithm of a power or product
  2. [A1] Obtain a correct linear equation in any form, e.g. (3x-1)ln2 = ln5+(1-x)ln3
  3. [M1] Solve for x
  4. [A1] Obtain final answer x = ln 30 / ln 24
  5. [M1] (Alternative method) Use laws of indices to split at least one exponential term
  6. [A1] (Alternative method) Obtain 24^x = 30
  7. [M1] (Alternative method) Solve for x
  8. [A1] (Alternative method) Obtain final answer x = ln 30 / ln 24

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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 3 Variant 2, question 1.

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