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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Oct/Nov 2021 · Q14 Marks

Find the value of x for which 3(2¹⁻ˣ) = 7ˣ. Give your answer in the form ln a / ln b, where a and b are integers.

  1. Find the value of x for which 3(2¹⁻ˣ) = 7ˣ. 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 2021). The mark or mark type is shown in brackets.

  1. [*M1] Use law of the logarithm of a product, a quotient or power
  2. [A1] e.g. ln3+(1-x)ln2 = x ln 7
  3. [DM1] Solve a linear equation for x
  4. [A1] Obtain answer x = ln 6 / ln 14
  5. Alternative method for Question 1
  6. [*M1] OE
  7. [A1] 6=2ˣ7ˣ [=14ˣ]
  8. [DM1] Use law of the logarithm of a power to solve for x
  9. [A1] Obtain answer x = ln 6 / ln 14

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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 2021 Paper 3 Variant 2, question 1.

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