Date: _______________________ Period: ____________ Name: ___________________________________

EL.3 Practice A Logarithmic Functions Write each exponential equation in logarithmic form. 1. 73 = 343

2. 26 = 64

3. 152 = 225

logbase 343 = exponent

logbase 64 = exponent

logbase 225 = exponent

log7 343 = __________

log2 64 = __________

log15 225 = __________

4. 23 = 8 ____________________ 7. 45 = 1024 ____________________

5. 170 = 1 ____________________ 8. 36 = 729 ____________________

6. 112 = 1 _____________________ 9. 54 = 625 _____________________

Write each logarithmic equation in exponential form. 10. log4 64 = 3

11. log8 512 = 3

12. log6 36 = 2

logbase 64 = exponent

logbase 512 = exponent

logbase 36 = exponent

_____________ = 64

_____________ = 512

_____________ = 36

13. log10 100 = 2 ____________________ 16. log2 128 = 7 ____________________

14. log5 125 = 3 ____________________ 17. log3 243 = 5 ____________________

15. log9 1 = 0 _____________________ 18. log100 1,000,000 = 3 _____________________

Evaluate by using mental math. 19. log 10,000

20. log 100,000

21. log 1

104 = 10,000

105 = 100,000

100 = 1

log 10,000 = ___________

log 100,000 = ___________

log 1 = ___________

22. log2 16 ____________________ 25. log100 100,000,000 ____________________ 28. log4 64

23. log4 1 ____________________ 26. log 1,000,000,000 ____________________ 29. log5 25

24. log9 81 _____________________ 27. log3 81 _____________________ 30. log 1000

EL.4 Practice A Properties of Logarithms Express as a single logarithm. Simplify, if possible. 1. log3 9 + log3 27

2. log2 16 + log2 4

3. log5 125 + log5 25

log3 (9 ∙ 27) = log3 243

log2 (16 ∙ 4) = log2 ____

log5 (125 ∙ 25)= log5 _____

3 x = 243, so x = ______

2x = ____, so x = ________

5x = _____, so x = ____

4. log10 250 + log10 40 ____________________

5. log6 3 + log6 2

6. log8 16 + log8 4

____________________

_____________________

Express as a single logarithm. Simplify, if possible. 7. log5 250 - log5 10 ____________________ 10. log4 128 - log4 8 ____________________

8. log3 21- log3 7

9. log2 160 - log2 5

____________________ 11. log6 72 - log6 2

_____________________ 12. log5 1000 - log5 8

____________________

_____________________

Simplify, if possible. 13. log6 362

14. log5 54

15. log2 83

2 log6 36

4 log5 5

3 log2 8

2 = 2 = _____________

___________________

___________________

16. log3 34 ____________________

17. log4 644

18. log8 82

____________________

_____________________

Evaluate. Round to the nearest hundredth. 19. log5 13 ____________________

20. log3 7

21. log8 21

____________________

Solve. 22. The Richter magnitude of an earthquake, M, is related to the 2

 E  . 11.8   10 

energy released in ergs, E, by the formula M  log  3

Find the energy released by an earthquake of magnitude 6.8.

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