A-level · Exponentials & logarithms

Solving exponential and logarithmic equationsExam-style questions

Taking logs to solve a^x = b, equations with e^x and ln, hidden quadratics in e^x or a^x, and log equations solved with the laws — always checking which roots are valid.

Start practising Read the lesson

14 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4
  1. 1
    (a) Solve the equation 32x+20=4×3x+13^{2x} + 20 = 4 \times 3^{x + 1}. Give your answers correct to 3 significant figures.

    (4 marks)
    (b) It is given that log⁡3(y+4)−log⁡3(2y−1)=2log⁡3x−1\log_{3}(y + 4) - \log_{3}(2y - 1) = 2\log_{3}x - 1.

    Express yy in terms of xx, in a form not involving logarithms.

    (4 marks)
    Level 4 · 8 marksTry it
  2. 2
    Solve 32x−1=403^{2x - 1} = 40, giving your answer to 3 significant figures.
    Level 4 · 2 marksTry it