plumiLogarithms and the laws of logs: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on F.2 Logarithms and the laws of logs, 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 8 questions on Logarithms and the laws of logs, as a list
- June 2025, Paper 1, Q3 (1 mark): Express log3 2x – log3 x as a single logarithm. Circle your answer. [1 mark] log3 1 2 log3 2 log3 x log3 2 x2
- June 2025, Paper 3, Q4 (3 marks): (a) State the value of loga a2 where a > 0 [1 mark] 4 (b) Find the value of loga √ a – loga 1 a2 where a > 0 [2 marks]
- June 2024, Paper 1, Q2 (1 mark): The function f is defined by f (x) = ex + 1 for x ℝ Find an expression for f –1(x) Tick (✓) one box. [1 mark] f –1(x) = ln (x – 1) f –1(x) = ln (x) – 1 f –1(x)
- June 2022, Paper 2, Q9 (4 marks): Given that log2 x3 − log2 y2 = 9 show that x = Ay p where A is an integer and p is a rational number. [4 marks]
- November 2020, Paper 3, Q8 (12 marks): The sum to infinity of a geometric series is 96 The first term of the series is less than 30 The second term of the series is 18 8 (a) Find the first term and c
- June 2019, Paper 1, Q1 (1 mark): Given that a > 0 , determine which of these expressions is not equivalent to the others. Circle your answer. [1 mark] −2 log10 1 a 2 log10 (a) log10 (a2) −4 log
- June 2018, Paper 1, Q4 (3 marks): The function f is defined by f (x) = e x−4, x 2 R Find f −1(x) and state its domain. [3 marks]
- 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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