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A-LevelMathematicsLogarithmic and exponential functions9709/22 · Oct/Nov 2018 · Q25 Marks

Given that 9x + 3x = 240, find the value of 3x and hence, using logarithms, find the value of x correct to 4 significant figures.

  1. (a)Given that 9x + 3x = 240, find the value of 3x and hence, using logarithms, find the value of x correct to 4 significant figures.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. B1 Recognise 9x as (3x)² or 32x
  2. *M1 Attempt solution of quadratic equation in 3x
  3. A1 Obtain, finally, 3x = 15 only
  4. M1 Apply logarithms and use power law for 3x = k where k > 0
  5. A1 Obtain 2.465
  6. May be implied by 3x (3x+1)(= 240)
  7. Perhaps using substitution u = 3x
  8. Dependent *M, need to see xln3=lnk, x = log3k oe
  9. May be done using 9x/2, same processes

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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, Oct/Nov 2018 Paper 2 Variant 2, question 2.

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