Lesson F5

F5 Solving exponential equations Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson F5, Solving exponential equations: 20 multiple choice questions for the AQA Maths (7357), Unit 6: Exponentials and logarithms, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Solve 2^x = 16.

    • x = 8
    • x = 2
    • x = 3
    • x = 4

  2. Solve 3^x = 1.

    • x = -1
    • x = 1
    • x = 0
    • x = 3

  3. Solve e^x = 0.5 exactly.

    • x = ln 2
    • x = 1/ln 2
    • x = -ln 2
    • x = 0.5

  4. Solve 5^x = 125.

    • x = 3
    • x = 25
    • x = 2
    • x = 5

  5. Which is the first step in solving 7^x = 30?

    • Take logarithms of both sides
    • Write 30 as 7 times 4 and cancel the 7
    • Divide both sides by 7 and then square the result
    • Subtract 7 from both sides of the equation

  6. Solve 4^x = 2^(x + 1).

    • x = 1
    • x = 1/2
    • x = 0
    • x = 2

  7. Solve 2^(3x) = 32.

    • x = 5
    • x = 15
    • x = 3/5
    • x = 5/3

  8. Solve 3^(2x - 1) = 27.

    • x = 5/2
    • x = 2
    • x = 3
    • x = 1

  9. Solve e^(2x) - 5e^x + 6 = 0.

    • x = 2 or x = 3
    • x = ln 2 or x = ln 3
    • x = 0 or x = ln 6
    • x = ln 5 or x = ln 6

  10. Solve 10^x = 4, giving x to 3 decimal places.

    • 0.398
    • 1.386
    • 0.602
    • 0.4

  11. Solve 2e^(-x) = 0.5 exactly.

    • x = 0.25
    • x = ln 0.25
    • x = ln 4
    • x = 1/ln 4

  12. Solve 5^x = 2^(x + 3) exactly.

    • x = ln(5/2)/3
    • x = 3 ln 2 / ln(5/2)
    • x = 3 ln 5 / ln 2
    • x = (ln 2 - ln 5)/3

  13. What is the smallest integer n for which 1.05^n is at least 2?

    • 20
    • 14
    • 2
    • 15

  14. A population is P = 2000 (1.03)^t. Approximately when does P reach 4000?

    • About 2 years
    • About 23.4 years
    • About 46.9 years
    • About 12 years

  15. Solve 4^x - 6 x 2^x + 8 = 0.

    • x = 2 or x = 4
    • x = 1 or x = 4
    • x = 1 or x = 2
    • x = 0 or x = 2

  16. Solve 3^x = 2^(x + 1) exactly.

    • x = 2 ln 3 / ln 2
    • x = ln 3 / ln 2
    • x = ln(3/2) / ln 2
    • x = ln 2 / ln(3/2)

  17. Solve 2^(x + 1) + 2^x = 12.

    • x = 2
    • x = 3
    • x = 1
    • x = log_10 12

  18. Which equation has no real solution?

    • e^x = -3
    • 10^x = 0.001
    • e^x = 3
    • 2^x = 1

  19. Solve (1/2)^x = 8.

    • x = -3
    • x = 1/3
    • x = 3
    • x = -8

  20. Solve 9^x - 4 x 3^x + 3 = 0.

    • x = 0 or x = 3
    • x = 0 only
    • x = 1 or x = 3
    • x = 0 or x = 1

All AQA Maths quizzes