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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Feb/Mar 2019 · Q15 Marks

Show that the equation log10(x - 4) = 2 – log10 x can be written as a quadratic equation in x.

  1. (i)Show that the equation log10(x - 4) = 2 – log10 x can be written as a quadratic equation in x.[3]
  2. (ii)Hence solve the equation log10(x - 4) = 2 – log10 x, giving your answer correct to 3 significant figures.[2]

Mark scheme

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

  1. [M1] Use law for the logarithm of a product or quotient
  2. [M1] Use log10100 = 2 or 10² =100
  3. [A1] Obtain x²-4x-100 = 0, or equivalent
  4. [M1] Solve a 3-term quadratic equation
  5. [A1] Obtain answer 12.2 only

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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, Feb/Mar 2019 Paper 3 Variant 2, question 1.

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