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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Ren uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 72?

   1.857
2. 2.

   Tala uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 0.75?

   -0.125
3. 3.

   Zee uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 1.2?

   0.079
4. 4.

   Bo uses log 3 ≈ 0.477 and log 5 ≈ 0.699 from a math book. To the nearest thousandth, what is log 45?

   1.653
5. 5.

   Esme expands log₃ (√x · y²/27) in a math book. Which choice is equal to it?

   • (1/2) log₃ x + 2 log₃ y − 3
   • (1/2) log₃ x + 2 log₃ y + 3
   • 3 − (1/2) log₃ x − 2 log₃ y
   • (log₃ x)^(1/2) + (log₃ y)² − 3
6. 6.

   Jun expands log₂ (4x/(y + 1)) on a math club card. Which choice is equal to it?

   • 2 + log₂ x − log₂ (y + 1)
   • 2 + log₂ x + log₂ (y + 1)
   • 2 + log₂ x − log₂ y − log₂ 1
   • 4 + log₂ x − log₂ (y + 1)
7. 7.

   Luz expands log₂ √(x/16) in a math book. Which choice is equal to it?

   • (1/2) log₂ x − 2
   • (log₂ x − 4)^(1/2)
   • (1/2) log₂ x − 4
   • 2 − (1/2) log₂ x
8. 8.

   Milo writes (1/2) log x − 3 log y + log 4 as one log on a math club card. Which choice is it?

   • log (2x/(3y))
   • log (√x − y³ + 4)
   • log (4√x/y³)
   • log (y³/(4√x))
9. 9.

   Noah writes 2 log₃ x + log₃ 9 − log₃ (x + 1) as one log in a math book. Which choice is it?

   • log₃ ((x + 1)/(9x²))
   • log₃ (18x/(x + 1))
   • log₃ (9x²/(x + 1))
   • log₃ (x² + 9 − (x + 1))
10. 10.

    Pia writes (1/3) log₂ x + 2 log₂ y as one log on the class board. Which choice is it?

    • log₂ (∛x + y²)
    • log₂ (2xy/3)
    • log₂ (2y∛x)
    • log₂ (y²∛x)