plumiSolving exponential and log equations: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on F.3 Solving exponential and log equations, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 11 questions on Solving exponential and log equations, as a list
- June 2025, Paper 2, Q4 (2 marks): Solve the equation 5x–1 = 20 Give your answer in an exact form. [2 marks]
- June 2024, Paper 2, Q4 (3 marks): Use logarithms to solve the equation 5x–2 = 71570 Give your answer to two decimal places. [3 marks]
- June 2024, Paper 2, Q8 (7 marks): A zookeeper models the median mass of infant monkeys born at their zoo, up to the age of 2 years, by the formula y = a + b log10 x where y is the median mass in
- June 2024, Paper 3, Q8 (8 marks): The temperature θ °C of an oven t minutes after it is switched on can be modelled by the equation θ = 20(11 – 10e–kt) where k is a positive constant. Initially
- June 2023, Paper 1, Q6 (5 marks): Show that the equation 2 log10 x = log10 4 + log10 (x + 8) has exactly one solution. Fully justify your answer. [5 marks]
- November 2021, Paper 2, Q6 (4 marks): Show that the solution of the equation 5x = 3x+4 can be written as x = ln 81 ln 5 − ln 3 Fully justify your answer. [4 marks]
- November 2020, Paper 1, Q15 (10 marks): The region enclosed between the curves y = ex, y = 6 × e x 2 and the line x = 0 is shown shaded in the diagram below. y y = e x x O y = 6 – e x 2 Show that the
- November 2020, Paper 3, Q5 (9 marks): The number of radioactive atoms, N, in a sample of a sodium isotope after time t hours can be modelled by N = N0e−kt where N0 is the initial number of radioacti
- June 2019, Paper 3, Q8 (12 marks): A student is conducting an experiment in a laboratory to investigate how quickly liquids cool to room temperature. A beaker containing a hot liquid at an initia
- June 2018, Paper 1, Q10 (8 marks): A scientist is researching the effects of caffeine. She models the mass of caffeine in the body using m = m0e−kt where m0 milligrams is the initial mass of caff
- June 2018, Paper 3, Q7 (5 marks): (a) Given that loga y = 2 loga 7 + loga 4 + 1 2 , find y in terms of a. [4 marks] 7 (b) When asked to solve the equation 2 loga x = loga 9 − loga 4 a student gi
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