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.

   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
2. 2.

   Pia uses log 3 ≈ 0.477 and log 5 ≈ 0.699 from a math book. To the nearest thousandth, what is log 15?

   1.176
3. 3.

   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
4. 4.

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

   0.954
5. 5.

   Bo uses log 2 ≈ 0.301 from a math book. To the nearest thousandth, what is log 8?

   0.903
6. 6.

   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 + (log₂ x)³ − log₂ y
   • (3 + 3 log₂ x) ÷ log₂ y
7. 7.

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

   • 2 · log₃ (x + 2)
   • 2 + log₃ (x + 2)
   • 9 + log₃ (x + 2)
   • 2 + log₃ x + log₃ 2
8. 8.

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

   • 2 − 2 log₅ x
   • 2 log₅ x − 2
   • 2 log₅ x + 2
   • (log₅ x)² − 2
9. 9.

   Noah writes 3 log₂ x − log₂ 4 as one log on the class board. Which choice is it?

   • log₂ (3x/4)
   • log₂ (x³ − 4)
   • log₂ (4/x³)
   • log₂ (x³/4)
10. 10.

    Pia writes log₃ x + log₃ (x + 1) as one log on a math club card. Which choice is it?

    • (log₃ x)(log₃ (x + 1))
    • log₃ (2x + 1)
    • log₃ (x² + 1)
    • log₃ (x² + x)