Exponential form and logarithmic form, evaluating logarithms, and change of base

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Row 0: 1; row 1: 3; row 2: 9; the rows go on. Bo starts a growth table at 1 and multiplies by 3 on each arrow. What is log₃ 81, the row number that gives 81?

   4
2. 2.

   Row 0: 1; row 1: 2; row 2: 4; the rows go on. Esme starts a growth table at 1 and multiplies by 2 on each arrow. What is log₂ 64, the row number that gives 64?

   6
3. 3.

   Row 0: 1; row 1: 5; row 2: 25; the rows go on. Jun starts a growth table at 1 and multiplies by 5 on each arrow. What is log₅ 125, the row number that gives 125?

   3
4. 4.

   Kira reads 2⁵ = 32 in a math book. Which choice writes 2⁵ = 32 in logarithm form?

   • log₅ 32 = 2
   • log₂ 32 = 5
   • log₃₂ 2 = 5
   • log₂ 5 = 32
5. 5.

   Luz reads 3⁴ = 81 in a math book. Which choice writes 3⁴ = 81 in logarithm form?

   • log₄ 81 = 3
   • log₃ 4 = 81
   • log₃ 81 = 4
   • log₈₁ 3 = 4
6. 6.

   Noah writes log₅ 125 = 3 on the class board. Which choice writes log₅ 125 = 3 as a power?

   • 125³ = 5
   • 3⁵ = 125
   • 5³ = 125
   • 5¹²⁵ = 3
7. 7.

   Pia finds log₆ 36 = 2 in a math book. Which choice writes log₆ 36 = 2 as a power?

   • 2⁶ = 36
   • 6² = 36
   • 36² = 6
   • 6³⁶ = 2
8. 8.

   Ren writes log 100 = 2 in a notebook. Which choice writes log 100 = 2 as a power?

   • 10² = 100
   • 10¹⁰⁰ = 2
   • 100² = 10
   • 2¹⁰ = 100
9. 9.

   Zee checks a math book answer for log₃ 243. What is log₃ 243?

   5
10. 10.

    Ari writes log 10000 on the class board. What is log 10000?

    4