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A-LevelMathematicsLogarithmic and exponential functions9709/33 · May/June 2022 · Q35 Marks

Show that the equation log₃(2x + 1) = 1 + 2log₃(x – 1) can be written as a quadratic equation in x.

  1. (a)Show that the equation log₃(2x + 1) = 1 + 2log₃(x – 1) can be written as a quadratic equation in x.[3]
  2. (b)Hence solve the equation log₃ (4y + 1) = 1 + 2 log₃(2y – 1), giving your answer correct to 2 decimal places.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

  1. [M1] Use law of logarithm of a power
  2. [B1] Use log₃3 = 1
  3. [A1] Obtain 3x²−8x+2=0 or 1.5x² − 4x+1=0
  4. [M1] Solve 3-term quadratic equation from part 3(a) or restart to find y
  5. [A1] Obtain answer 1.19

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2022 Paper 3 Variant 3, question 3.

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