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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · Oct/Nov 2011 · Q1110 Marks

Solve 5^(2x+3) / 25^(2x) = 25^(2-x) / 125^x.

  1. (a)(i)Solve 5^(2x+3) / 25^(2x) = 25^(2-x) / 125^x.[3]
  2. (a)(ii)Solve lg y + lg(y – 15) = 2.[4]
  3. (b)Without using a calculator, and showing each stage of your working, find the value of 2 log₁₂ 4 - (1/2) log₁₂ 81 + 4 log₁₂ 3.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [1] Express in powers of 5.
  2. [1] 5^(2x+3) / 5^(4x) = 5^(2(2-x)) / 5^(3x)
  3. [1] Use rules of indices (2x + 3 – 4x = 2(2 – x) – 3x)
  4. [1] x = 1/3
  5. [1] LHS = lg y(y – 15)
  6. [1] 2 = lg 100
  7. [1] Solve 3 term quadratic
  8. [1] 20 only
  9. [1] log₁₂ 16 - log₁₂ 9 + log₁₂ 81
  10. [1] Correctly combine 3 logarithms
  11. [1] 2

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 2 Variant 1, question 11.

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