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

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   In Kira's × 2 growth table, 4 is row 2 and 32 is row 5. What is log₂ (4 × 32)?

   7
2. 2.

   In Luz's × 2 growth table, 128 is row 7 and 8 is row 3. What is log₂ (128 ÷ 8)?

   4
3. 3.

   In Milo's × 3 growth table, 2187 is row 7 and 9 is row 2. What is log₃ (2187 ÷ 9)?

   5
4. 4.

   Noah knows that log₃ 9 = 2. What is log₃ (9⁵)?

   10
5. 5.

   Pia knows that log 1000 = 3. What is log (1000²)?

   6
6. 6.

   Tala expands log₅ (7x) on a math club card. Which choice is equal to log₅ (7x)?

   • log₅ 7 − log₅ x
   • log₅ 7 · log₅ x
   • log₅ 7 + log₅ x
   • 7 log₅ x
7. 7.

   Zee expands log₃ (x/4) in a math book. Which choice is equal to log₃ (x/4)?

   • log₃ 4 − log₃ x
   • log₃ x − log₃ 4
   • log₃ x ÷ log₃ 4
   • log₃ x + log₃ 4
8. 8.

   Ari expands log₂ (x⁵) on the class board. Which choice is equal to log₂ (x⁵)?

   • x log₂ 5
   • 5 log₂ x
   • (log₂ x)⁵
   • log₂ (5x)
9. 9.

   Bo writes log₂ x + log₂ 5 as one log on a math club card. Which choice is it?

   • log₂ (x/5)
   • log₂ (x + 5)
   • log₂ (5x)
   • (log₂ x)(log₂ 5)
10. 10.

    Jun writes 3 log₅ x as one log on the class board. Which choice is it?

    • log₅ (x³)
    • (log₅ x)³
    • log₅ (3x)
    • log₅ (x + 3)