Laws of Logarithms Worksheet

If and , determine the value of:

1. 2.

3. 4.

5. If and , determine an expression for the following in terms of and : 6. 7.

8. 9. 10. 11. 12. If and , determine an expression for the following in terms of and : 13. 14. 15. 16. 17.

18. If and , determine an expression for

.

19. If , determine an expression for .

If , determine an expression for the following in terms of :

20. 21.

22. 23.

24. 25. Write as a single logarithm: 26. 27.

28. 29.

30.

3log =a 7log =b

2logab ba

log

ba 2

logab10

log

ba

100log

a=3log b=5log

a b15log 75log

45log 325

log

30log 6log

500log

x=5log2 y=3log2x y

20log2 24log25.7log2 5.4log28.0log2

x=5log3 y=36log26log5log 29 −

a=25log4 5log25log 162 +

k=8log3 k2log3 8log9

64log3 24log93log8 27log24

cba logloglog −− alog2 −

3log2 +b 2log2log 55 +− bc

pk 33 log3log2 −−

Answers: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27. 28.

29. 30.

17 4−1− 56− ba +ba 2+ 52 +aab −2 1+aba −+1 b+2

x+2 y+31−+ yx 12 −y

x−2 22yx

−

42 aa + k

31

2k

k2

21+k

k1

k+13

bca

log

a100

log b8log2

!"

#$%

&25

25log

bc

!!"

#$$%

&

pk27

log2

3