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A-LevelMathematicsLogarithmic and exponential functions9709/33 · Oct/Nov 2019 · Q34 Marks

Showing all necessary working, solve the equation (3^(2x) + 3^(-x)) / (3^(2x) - 3^(-x)) = 4. Give your answer correct to 3 decimal places.

  1. Showing all necessary working, solve the equation (3^(2x) + 3^(-x)) / (3^(2x) - 3^(-x)) = 4. Give your answer correct to 3 decimal places.[4]

Mark scheme

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

  1. [M1] Reduce the equation to a horizontal equation in 3^(3x), 3^(3x+1) or 27^x
  2. [A1] Simplify and reach 3(3^(3x)) = 5, 3(27^x) = 5, or equivalent
  3. [M1] Use correct method for finding x from a positive value of 3^(3x), 3^(3x+1) or 27^x
  4. [A1] Obtain answer x = 0.155

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 3 Variant 3, question 3.

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