Properties of logarithms: product, quotient and power, expanding and condensing

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Kira works out log₆ 4 + log₆ 9 on the class board. What is log₆ 4 + log₆ 9?

   2
2. 2.

   Luz works out log₂ 40 − log₂ 5 on the class board. What is log₂ 40 − log₂ 5?

   3
3. 3.

   Noah uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 6?

   0.778
4. 4.

   Ren uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 1.5?

   0.176
5. 5.

   Tala uses log 3 ≈ 0.477 and log 5 ≈ 0.699 from a math book. To the nearest thousandth, what is log 0.6?

   -0.222
6. 6.

   Zee uses log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 9?

   0.954
7. 7.

   Esme expands log₂ (8x³/y) fully on a math club card. Which choice is equal to it?

   • (3 + 3 log₂ x) ÷ log₂ y
   • 3 + 3 log₂ x − log₂ y
   • 3 + 3 log₂ x + log₂ y
   • 3 + (log₂ x)³ − log₂ y
8. 8.

   Jun expands log₃ (9(x + 2)) in a math book. Which choice is equal to it?

   • 2 · log₃ (x + 2)
   • 9 + log₃ (x + 2)
   • 2 + log₃ x + log₃ 2
   • 2 + log₃ (x + 2)
9. 9.

   Kira expands log₅ (x²/25) on the class board. Which choice is equal to it?

   • (log₅ x)² − 2
   • 2 log₅ x − 2
   • 2 − 2 log₅ x
   • 2 log₅ x + 2
10. 10.

    Luz expands log₂ (16/(x + 3)) on a math club card. Which choice is equal to it?

    • 4 − log₂ x − log₂ 3
    • 4 − log₂ (x + 3)
    • 4 ÷ log₂ (x + 3)
    • log₂ (x + 3) − 4