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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2012 · Q46 Marks

Given that logₐ pq = 9 and logₐ p²q = 15, find the value of

  1. (i)logₐ p and of logₐ q,[4]
  2. (ii)logₚ a + log q a.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [B1] logₐ p + logₐ q = 9
  2. [B1] 2 logₐ p + logₐ q = 15
  3. [M1] M1 for solution of the two equations
  4. [A1] A1 for both
  5. [B1] Or a⁹ = pq
  6. [B1] a¹⁵ = p²q
  7. [M1] M1 for complete solution of the two equations
  8. [A1] A1 for obtaining both in correct log form
  9. [M1] Or logₐ p²q – logₐ pq = 6
  10. [B1] B1 for logₐ (p²q/pq) = 6
  11. [B1] B1 for logₐ pq = logₐ p + logₐ q = 9
  12. [A1] A1 for both
  13. [M1, A1] M1 for change of both to base a logarithm

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 1 Variant 2, question 4.

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