Lesson F4

F4 Laws of logarithms Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F4, Laws of logarithms: 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. Which is the product law of logarithms?

    • log_a x + log_a y = log_a(xy)
    • log_a(x + y) = log_a x + log_a y
    • log_a x x log_a y = log_a(x + y)
    • log_a x - log_a y = log_a(xy)

  2. Which is the quotient law of logarithms?

    • log_a x - log_a y = log_a(x - y)
    • log_a x - log_a y = log_a(x/y)
    • log_a x - log_a y = log_a(xy)
    • log_a x / log_a y = log_a(x/y)

  3. Which is the power law of logarithms?

    • k log_a x = log_a(kx)
    • k log_a x = log_a(x + k)
    • k log_a x = log_a(x^k)
    • k log_a x = (log_a x)^k

  4. Simplify log_2 12 - log_2 3.

    • log_2 9
    • 2
    • 4
    • 1

  5. Simplify log_10 5 + log_10 2.

    • 0.5
    • log_10 7
    • log_10 3
    • 1

  6. Write 3 log_a 2 as a single logarithm.

    • log_a 5
    • log_a 6
    • log_a 8
    • log_a 23

  7. What is log_a(1) for a > 0 and a not equal to 1?

    • a
    • 0
    • 1
    • undefined

  8. Simplify log_3 81 - 2 log_3 3.

    • 1
    • 4
    • 0
    • 2

  9. Express log_5(x^2 y) in terms of log_5 x and log_5 y.

    • 2(log_5 x + log_5 y)
    • log_5 x^2 - log_5 y
    • 2 log_5 x + log_5 y
    • log_5 x + log_5 y

  10. Given log_a 2 = p and log_a 3 = q, express log_a 6 in terms of p and q.

    • p/q
    • pq
    • 2p + 3q
    • p + q

  11. Given log 2 = 0.301 (base 10), find log 16 to 3 decimal places.

    • 0.301^4
    • 1.204
    • 3.010
    • 0.602

  12. Evaluate (log_2 16)/(log_2 4).

    • 2
    • 1/2
    • 8
    • 4

  13. Solve log_2 x - log_2(x - 2) = 2, with x > 2.

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

  14. Simplify log_a(a^3 b) - log_a b.

    • 3
    • log_a(a^3 b)
    • 2
    • 3 + log_a b

  15. Solve 2 log_10 x - log_10 4 = log_10 9, with x > 0.

    • x = 4.5
    • x = 18
    • x = 3
    • x = 6

  16. Which expression is equivalent to log_a(x^2/y) for x, y > 0?

    • (2 log_a x)/(log_a y)
    • 2 log_a x + log_a y
    • 2 log_a x - log_a y
    • log_a x^2 + log_a y

  17. Which statement about log_a(x + y) is true in general?

    • log_a(x + y) is not equal to log_a x + log_a y in general
    • log_a(x + y) equals log_a x divided by log_a y
    • log_a(x + y) always equals log_a x + log_a y
    • log_a(x + y) equals log_a x times log_a y

  18. Simplify log_2 8 + log_2(1/4).

    • -1
    • 1
    • 5
    • 2

  19. Solve log_2(x + 1) - log_2(x - 1) = 1, with x > 1.

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

  20. Given that 2 log_a 3 - log_a 2 = log_a k, find k.

    • k = 7
    • k = 6
    • k = 9/2
    • k = 2/9

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