Lesson F3

F3 Logarithms as the inverse of exponentials Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F3, Logarithms as the inverse of exponentials: 20 multiple choice questions for the AQA Maths (7357), Unit 6: Exponentials and logarithms, written with Revision Ninja.

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The 20 questions

  1. What is log base 2 of 8?

    • 3
    • 4
    • 1/3
    • 2

  2. What is log base a of a, for a > 0 and a not equal to 1?

    • a
    • a^2
    • 0
    • 1

  3. What is log base 10 of 0.001?

    • -1
    • -3
    • 3
    • -2

  4. Which statement is equivalent to 2^5 = 32?

    • log base 32 of 2 = 5
    • log base 2 of 32 = 5
    • log base 2 of 5 = 32
    • log base 5 of 32 = 2

  5. What is the inverse function of y = e^x?

    • y = 1/e^x
    • y = x^e
    • y = log base 10 of x
    • y = ln x

  6. What is the value of e^(ln x) for x > 0?

    • x
    • 1
    • e x
    • ln x

  7. Which domain restriction applies to log base a of x for a > 0 and a not equal to 1?

    • All real values of x
    • x < 0
    • x >= 0 only
    • x > 0

  8. Solve log base 3 of x = 4.

    • x = 12
    • x = 81
    • x = 64
    • x = 7

  9. Evaluate log base 5 of 1/25.

    • -5
    • -2
    • 2
    • -1/2

  10. Solve ln x = 3 exactly.

    • x = 3e
    • x = ln 3
    • x = e^(1/3)
    • x = e^3

  11. What is the value of log base 4 of 2?

    • 4
    • 1/2
    • 1/4
    • 2

  12. If 3^x = 20, which expression gives x?

    • x = ln 20 / ln 3
    • x = ln 3 / ln 20
    • x = 20/3
    • x = 3 ln 20

  13. Solve 10^x = 7, giving x to 2 decimal places.

    • 0.85
    • 0.15
    • 1.85
    • 0.70

  14. Solve e^(2x) = 9 exactly.

    • x = ln 3
    • x = e^(9/2)
    • x = 2 ln 9
    • x = 4.5

  15. For f(x) = ln x and g(x) = e^x, which statement about f(g(x)) is correct?

    • f(g(x)) = 1 for all x
    • f(g(x)) = e x
    • f(g(x)) = x for all real x
    • f(g(x)) = e^x ln x

  16. Solve log base 2 of (x + 1) + log base 2 of (x - 1) = 3, with x > 1.

    • x = sqrt(7)
    • x = -3
    • x = 3
    • x = 9

  17. For a > 0 and a not equal to 1, through which point does y = log base a of x always pass?

    • (a, a)
    • (0, 1)
    • (0, 0)
    • (1, 0)

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

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

  19. What is the inverse function of y = 2^x + 1?

    • y = log base 2 of (x + 1)
    • y = (log base 2 of x) - 1
    • y = log base 2 of (x - 1), for x > 1
    • y = log base 2 of x + 1

  20. Solve log base 10 of x + log base 10 of (x - 3) = 1, with x > 3.

    • x = 5
    • x = 2
    • x = -2
    • x = 10

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