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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/11 · May/June 2019 · Q78 Marks

Solve log₃x+log₉x = 12.

  1. (a)Solve log₃x+log₉x = 12.[3]
  2. (b)Solve log₄ (3y² - 10) = 2log₄(y-1) + 1/2.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] change to base 3 logarithm log₃x / log₃9
  2. [M1] simplification and dealing with base 3 logarithms to obtain a power of 3
  3. [A1] x = 6561
  4. [B1] use of power rule
  5. [B1] for log₄2
  6. [M1] Dep on first two B marks simplification to a three term quadratic.
  7. [A1] y = 2 only
  8. [B1] use of division rule

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2019 Paper 1 Variant 1, question 7.

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