EVALUATING LOGARITHMS WORKSHEET

Evaluate each of the following logarithms without the use of a calculator.

Problem 1 :

log₃ 81

Problem 2 :

Problem 3 :

log₁₂ 144

Problem 4 :

Problem 5 :

Problem 6 :

log_0.25 4

Problem 7 :

log₈ 4

Problem 8 :

Problem 9 :

Problem 10 :

log₁₀ 1

Problem 11 :

Problem 12 :

Problem 13 :

log₉ 3

Problem 14 :

Problem 15 :

log₁₂₈ 2

Problem 16 :

Problem 17 :

ln e¹²

Problem 18 :

Problem 19 :

ln 1

Problem 20 :

e^{ln 4}

Problem 21 :

log₂ 16√2

Problem 22 :

log₃ ⁵√9

Problem 23 :

log₃ (9 ⋅ ³√3)

Problem 24 :

Problem 25 :

Answers

1. Answer  :

= log₃ 81

= log₃ (3⁴)

= 4log₃ 3

= 4(1)

= 4

2. Answer  :

3. Answer  :

= log₁₂ 12²

= 2log₁₂ 12

= 2(1)

= 2

4. Answer  :

5. Answer  :

6. Answer  :

7. Answer  :

8. Answer  :

9. Answer  :

10. Answer  :

The value of logarithm of 1 to any base is equal to zero.

log₁₀ 1 = 0

11. Answer  :

12. Answer  :

13. Answer  :

14. Answer  :

15. Answer  :

16. Answer  :

17. Answer  :

= ln e¹²

= 12ln e

= 12(1)

= 12

18. Answer  :

19. Answer  :

The value of logarithm of 1 to any base is equal to zero.

ln 1 = 0

20. Answer  :

e^{ln 4} = 4

21. Answer  :

= log₂ 16√2

22. Answer  :

= log₃ ⁵√9

23. Answer  :

= log₃ (9 ⋅ ³√3)

24. Answer  :

25. Answer  :

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