plumiLogarithms and the laws of logs: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 6.2 Logarithms and the laws of logs, 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.
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All 12 questions on Logarithms and the laws of logs, as a list
- 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 2024, AS Pure, Q9 (5 marks): p = loga 16 q = loga 25 where a is a constant. Find in terms of p and/or q, (a) loga 256 (1) (b) loga 100 (2) (c) loga 80 × loga 3.2 (2)
- June 2023, Pure 1, Q6 (6 marks): a = log2 x b = log2(x + 8) Express in terms of a and/or b (a) log2 x (1) (b) log2(x 2 + 8x) (2) (c) log2 8 64 x Give your answer in simplest form. (3)
- 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, Q5 (6 marks): The table below shows corresponding values of x and y for y = log3 2x The values of y are given to 2 decimal places as appropriate. x 3 4.5 6 7.5 9 y 1.63 2 2.2
- 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 2, Q3 (3 marks): Using the laws of logarithms, solve the equation log3 (12y + 5) – log3 (1 – 3y) = 2 (3)
- November 2021, Statistics, Q6 (7 marks): The discrete random variable X has the following probability distribution x a b c P(X = x) log36 a log36 b log36 c where • a, b and c are distinct integers (a <
- 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
- June 2019, Pure 1, Q9 (5 marks): Given that a b 0 and that a and b satisfy the equation log a – log b = log(a – b) (a) show that a b b = − 2 1 (3) (b) Write down the full restriction on the val
- June 2019, Pure 2, Q8 (6 marks): (i) Find the value of 20 1 2 4 × ⎛ ⎝⎜ ⎞ ⎠⎟ = ∞ ∑ r r (3) (ii) Show that log5 1 48 2 1 2 n n n + + ⎛ ⎝⎜ ⎞ ⎠⎟= =∑ (3)
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