Lesson 1.06g

1.06g Solving exponential equations Quiz: OCR Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson 1.06g, Solving exponential equations: 20 multiple choice questions for the OCR Maths (H240), 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 = 8.

    • 2
    • 8
    • 3
    • 4

  2. Solve 3^x = 1.

    • 0
    • 1
    • -1
    • 3

  3. For a > 0 and a not 1, what is the solution of a^x = b?

    • x = a ln b
    • x = b / a
    • x = ln b / ln a
    • x = ln a / ln b

  4. What is the standard algebraic step to solve the equation 5^x = 12?

    • Divide by 5
    • Take natural logarithms
    • Differentiate both sides
    • Square both sides

  5. Solve 2^x = 1/16.

    • x = 4
    • x = -4
    • x = -1/4
    • x = -16

  6. Solve 2^x = 32^(x - 1).

    • x = 4/5
    • x = 5/4
    • x = -5/4
    • x = 5/6

  7. Solve 4^x = 8.

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

  8. Solve 5^(2x - 1) = 125.

    • x = 2
    • x = 3/2
    • x = 1
    • x = 4

  9. Solve 3^x = 20 to 2 decimal places.

    • x = 3.00
    • x = 2.73
    • x = 6.67
    • x = 1.30

  10. Solve 2^x = (1/2)^(x + 1).

    • x = -1
    • x = 1/2
    • x = -2
    • x = -1/2

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

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

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

    • x = 4
    • x = 1
    • x = 3
    • x = 2

  13. Solve 4^x - 2^(x + 1) - 8 = 0.

    • x = 2
    • x = 3
    • x = 4
    • x = -2

  14. Solve 10^(2x) - 3 x 10^x + 2 = 0.

    • x = 1 or x = log_2 10
    • x = 0 or x = log_10 2
    • x = 0 or x = 2
    • x = 0 only

  15. Solve 5^x = 3 x 2^x exactly.

    • x = ln 5 / ln 2
    • x = ln 3 / ln 2.5
    • x = 2.5 / 3
    • x = ln 3

  16. Solve 9^x = 27^(x + 1).

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

  17. For a > 0 with a not 1, when does a^x = b have a real solution?

    • When b < 0
    • When b = 0
    • When b > 0
    • When a > b

  18. Solve 2^x x 4^x = 64.

    • x = 1
    • x = 6
    • x = 2
    • x = 3

  19. Solve 10^x = 0.01.

    • x = 2
    • x = -0.01
    • x = -2
    • x = -1

  20. Solve e^x = 5.

    • x = 2 ln 5, about 3.22
    • x = ln 10, about 2.30
    • x = e^5, about 148.41
    • x = ln 5, about 1.61

All OCR Maths quizzes