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A-LevelMathematicsLogarithmic and exponential functions9709/32 · Oct/Nov 2020 · Q35 Marks

The variables x and y satisfy the relation 2ʸ = 3¹⁻²ˣ.

  1. (a)By taking logarithms, show that the graph of y against x is a straight line. State the exact value of the gradient of this line.[3]
  2. (b)Find the exact x-coordinate of the point of intersection of this line with the line y = 3x. Give your answer in the form ln a ln b , where a and b are integers.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

  1. [B1] State or imply y log2 = log3 - 2x log 3
  2. [B1] State that the graph of y against x has an equation which is linear in x and y, or is of the form ay = bx + c
  3. [B1] Clear indication that the gradient is -2 ln 3 / ln 2
  4. [M1] Substitute y = 3x in an equation involving logarithms and solve for x
  5. [A1] Obtain answer x = ln 3 / ln 72

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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 2020 Paper 3 Variant 2, question 3.

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