Solving exponential and log equations: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on 6.3 Solving exponential and log equations, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 19 questions on Solving exponential and log equations, as a list

June 2025, Pure 2, Q3 (2 marks): Given that 3 x = 7 y find the exact value of x y (2)
June 2025, AS Pure, Q10 (5 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Solve the equation 2 log3 (x
June 2025, AS Pure, Q13 (12 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The growth of a particular tr
June 2023, Pure 2, Q3 (5 marks): Given that log2(x + 3) + log2(x + 10) = 2 + 2 log2 x (a) show that 3x 2 – 13x – 30 = 0 (3) (b) (i) Write down the roots of the equation 3x 2 – 13x – 30 = 0 (ii)
June 2023, AS Pure, Q9 (5 marks): Using the laws of logarithms, solve the equation 2 3 2 2 5 5 log log x x (5)
June 2022, Pure 2, Q2 (4 marks): (a) Sketch the curve with equation y = 4 x stating any points of intersection with the coordinate axes. (2) (b) Solve 4 x = 100 giving your answer to 2 decimal
June 2022, AS Pure, Q8 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The air pressure, P kg/cm2, i
June 2022, AS Pure, Q9 (6 marks): (a) Given that p = log3 x, where x > 0, find in simplest form in terms of p, (i) log3 x 9     (ii) log3 x ( ) (2) (b) Hence, or otherwise, solve 2 log3 x
November 2021, Pure 1, Q8 (9 marks): A scientist is studying the growth of two different populations of bacteria. The number of bacteria, N, in the first population is modelled by the equation N =
November 2021, Pure 2, Q3 (3 marks): Using the laws of logarithms, solve the equation log3 (12y + 5) – log3 (1 – 3y) = 2 (3)
November 2021, AS Pure, Q11 (6 marks): The owners of a nature reserve decided to increase the area of the reserve covered by trees. Tree planting started on 1st January 2005. The area of the nature r
November 2020, Pure 1, Q2 (3 marks): By taking logarithms of both sides, solve the equation 43 p −1 = 5210 giving the value of p to one decimal place. (3)
November 2020, Pure 2, Q3 (5 marks): (a) Given that 2 log (4 − x) = log (x + 8) show that x2 − 9x + 8 = 0 (3) (b) (i) Write down the roots of the equation x2 − 9x + 8 = 0 (ii) State which of the ro
November 2020, Pure 2, Q5 (4 marks): The curve with equation y = 3 × 2 x meets the curve with equation y = 15 − 2 x+1 at the point P. Find, using algebra, the exact x coordinate of P. (4)
November 2020, Pure 2, Q9 (6 marks): A quantity of ethanol was heated until it reached boiling point. The temperature of the ethanol, θ °C, at time t seconds after heating began, is modelled by the
November 2020, Pure 2, Q13 (6 marks): The function g is defined by g (x) = 3 7 2 ln( ) ln( ) x x − − x > 0 x ≠ k where k is a constant. (a) Deduce the value of k. (1) (b) Prove that gʹ (x) > 0 for a
November 2020, AS Pure, Q8 (9 marks): The temperature, θ °C, of a cup of tea t minutes after it was placed on a table in a room, is modelled by the equation θ = 18 + 65e −t 8 t  0 Find, according t
June 2019, AS Pure, Q14 (9 marks): The value of a car, £V, can be modelled by the equation V = 15 700e– 0.25t + 2300 t \, t . 0 where the age of the car is t years. Using the model, (a) find th
June 2018, Pure 1, Q12 (10 marks): The value, £V, of a vintage car t years after it was first valued on 1st January 2001, is modelled by the equation V = Ap t where A and p are constants Given th

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