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A-LevelMathematicsAlgebra9709/21 · May/June 2025 · Q26 Marks

Use logarithms to solve the inequality 4^x < 0.05. Give your answer in the form x < a, where the value of a is correct to 3 significant figures.

  1. (a)Use logarithms to solve the inequality 4^x < 0.05. Give your answer in the form x < a, where the value of a is correct to 3 significant figures.[2]
  2. (b)Solve the inequality |3x+8|<9.[3]
  3. (c)Hence state the integers that satisfy both of the inequalities in parts (a) and (b).[1]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

  1. [M1] Apply logarithms to both sides and use relevant logarithm property.
  2. [A1] Obtain x < ln(0.05)/ln(4) or equivalent and hence x < -2.16.
  3. [M1] Attempt solution of equations 3x +8=±9 or of quadratic equation (3x + 8)² = 9².
  4. [A1] Obtain values -17/3 and 1/3.
  5. [A1] Conclude -17/3 < x < 1/3.
  6. [B1] State -5, -4, -3 only.

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2025 Paper 2 Variant 1, question 2.

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