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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Feb/Mar 2024 · Q44 Marks

The positive numbers p and q are such that ln(p/q) = a and ln(q²p) = b. Express ln(p⁷q) in terms of a and b.

  1. The positive numbers p and q are such that ln(p/q) = a and ln(q²p) = b. Express ln(p⁷q) in terms of a and b.[4]

Mark scheme

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

  1. [B1] Obtain ln p - ln q = a
  2. [B1] Obtain ln p + 2 ln q = b
  3. [M1] Completed method to obtain ln(p⁷q)
  4. [A1] Obtain (13a + 8b) / 3

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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 3 Variant 2, question 4.

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