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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
