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
    Solve the equation

    8x+1=42x−18^{x+1} = 4^{2x-1}

    (4 marks)
    Level 2 · 4 marksTry it
  2. 2
    Find the set of values of xx for which 7x<32x−17^{x} < 3^{2x - 1}. Give your answer in a simplified exact form.

    (3 marks)
    Level 2 · 3 marksTry it
  3. 3
    Using logarithms, solve the equation

    72x−1=3x+4,7^{2x - 1} = 3^{x + 4},

    giving your answer correct to 3 significant figures.

    (3 marks)
    Level 2 · 3 marksTry it