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A-LevelMathematicsLogarithmic and exponential functions9709/31 · Oct/Nov 2022 · Q34 Marks

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

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 logarithm of a product or power
  2. [A1] Obtain a correct linear equation in any form, e.g. (3x−1) ln 2 = ln 5 − x ln 3
  3. [M1] Solve for x
  4. [A1] Obtain answer x = ln 10 / 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 1, question 3.

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