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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Esme rewrites 8 and 32 as powers of 2 to find log₈ 32. What is log₈ 32?

   5/3
2. 2.

   Jun rewrites 27 and 9 as powers of 3 to find log₂₇ 9. What is log₂₇ 9?

   2/3
3. 3.

   Kira rewrites 4 and 1/32 as powers of 2 to find log₄ (1/32). What is log₄ (1/32)?

   -5/2
4. 4.

   Luz rewrites 25 and 1/125 as powers of 5 to find log₂₅ (1/125). What is log₂₅ (1/125)?

   -3/2
5. 5.

   Milo uses the ln key on a calculator to solve e^x = 15. To the nearest hundredth, what is x?

   2.71
6. 6.

   Noah uses the ln key on a calculator to solve e^x = 40. To the nearest hundredth, what is x?

   3.69
7. 7.

   Ren uses the ln key on a calculator to solve e^x = 0.2. To the nearest hundredth, what is x?

   -1.61
8. 8.

   Tala finds log₄ 0.3 with a calculator, using log₄ 0.3 = log 0.3 ÷ log 4. To the nearest hundredth, what is log₄ 0.3?

   -0.87
9. 9.

   Bo finds log₁₂ 1000 with a calculator, using log₁₂ 1000 = log 1000 ÷ log 12. To the nearest hundredth, what is log₁₂ 1000?

   2.78
10. 10.

    Esme finds log₉ 0.4 with a calculator, using log₉ 0.4 = log 0.4 ÷ log 9. To the nearest hundredth, what is log₉ 0.4?

    -0.42