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.

   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
4. 4.

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

   • (log₃ x)^(1/2) + (log₃ y)² − 3
   • 3 − (1/2) log₃ x − 2 log₃ y
   • (1/2) log₃ x + 2 log₃ y + 3
   • (1/2) log₃ x + 2 log₃ y − 3
5. 5.

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

   • 4 + log₂ x − log₂ (y + 1)
   • 2 + log₂ x − log₂ (y + 1)
   • 2 + log₂ x − log₂ y − log₂ 1
   • 2 + log₂ x + log₂ (y + 1)
6. 6.

   Kira expands log (1000∛x/y⁴) on the class board. Which choice is equal to it?

   • 3 + (log x)^(1/3) − (log y)⁴
   • 3 + (1/3) log x − 4 log y
   • 3 + (1/3) log x + 4 log y
   • 4 log y − 3 − (1/3) log x
7. 7.

   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 (y³/(4√x))
   • log (√x − y³ + 4)
   • log (4√x/y³)
8. 8.

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

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

   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)
10. 10.

    Ren writes 3 log₅ x − 2 log₅ y − 1 as one log on a math club card. Which choice is it?

    • log₅ (3x/(10y))
    • log₅ (x³ − y² − 5)
    • log₅ (5y²/x³)
    • log₅ (x³/(5y²))