6.4.1 Laws of logarithms Quiz: Pearson Edexcel Maths, Unit 6

The 20 questions

1. What is the equivalent expression for log_a(x) + log_a(y)?

   • log_a(x / y)
   • log_a(x + y)
   • x log_a(y)
   • log_a(xy)

2. Simplify the logarithmic expression log_a(x) - log_a(y).

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

3. What is the simplified form of k log_a(x)?

   • (log_a(x))^k
   • k^x log_a(a)
   • log_a(kx)
   • log_a(x^k)

4. Evaluate log_a(1) for any valid base a.

   • 1
   • 0
   • a
   • undefined

5. Evaluate log_a(a) where a > 0 and a != 1.

   • undefined
   • 0
   • 1
   • a

6. What is the value of log_10(1000)?

   • 30
   • 2
   • 3
   • 100

7. Express log_2(32) as a single integer.

   • 5
   • 6
   • 16
   • 4

8. What is log_3(1 / 9) simplified?

   • -3
   • 1/2
   • -2
   • 2

9. Write 2 log_5(x) + log_5(y) as a single logarithm.

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

10. Combine log_3(18) - log_3(2) into a single logarithm.

    • log_3(9) / 2
    • log_3(16)
    • log_3(36)
    • log_3(9)

11. Solve the equation log_2(x) = 3 for x.

    • 9
    • 6
    • 8
    • 32

12. Find the value of x if log_x(8) = 3.

    • 4
    • 2
    • 3
    • 24

13. Evaluate log_4(8) using logarithm laws.

    • 4
    • 1.5
    • 0.75
    • 2

14. What is the expanded form of log_p(a^3 b^2)?

    • 3 log_p(a) - 2 log_p(b)
    • (3 log_p(a))(2 log_p(b))
    • 3 log_p(a) + 2 log_p(b)
    • 6 log_p(ab)

15. Expand log_7(x / y^4) completely.

    • log_7(x) - 4 log_7(y)
    • log_7(x) + 4 log_7(y)
    • log_7(4x) - log_7(y)
    • log_7(x) - log_7(y) / 4

16. Solve log_5(x) + log_5(2) = log_5(10) for x.

    • 2
    • 20
    • 8
    • 5

17. If log_10(x) = 2.5, what is the exact value of log_10(10x)?

    • 12.5
    • 25
    • 3.5
    • 5.0

18. Simplify log_a(x^3) - 3 log_a(x).

    • log_a(x^3)
    • 0
    • 1
    • 3 log_a(2x)

19. Which expression is identically equal to log_a(x^2 - y^2)?

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

20. What is the exact value of log_2(1 / 8)?

    • -3
    • -1/3
    • 3
    • 1/3

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