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.

   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
5. 5.

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

   0.903
6. 6.

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

   • 2 log₅ x + 2
   • 2 log₅ x − 2
   • (log₅ x)² − 2
   • 2 − 2 log₅ x
7. 7.

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

   • log₂ (x + 3) − 4
   • 4 − log₂ x − log₂ 3
   • 4 − log₂ (x + 3)
   • 4 ÷ log₂ (x + 3)
8. 8.

   Milo writes 2 log x + log 5 − log y as one log in a math book. Which choice is it?

   • log (5x²y)
   • log (x² + 5 − y)
   • log (5x²/y)
   • log (10x/y)
9. 9.

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

   • log₂ (x³/4)
   • log₂ (x³ − 4)
   • log₂ (4/x³)
   • log₂ (3x/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 (x² + x)
    • log₃ (x² + 1)
    • log₃ (2x + 1)