Name_______________________________________Date__________________
Algebra 2
Logarithm Properties Worksheet
For problems 1 – 10, write as a single logarithm and simplify it.
2
1. log 4 48 log 4 ( ) log 4 8
2. log8 24 log 8 4 log 8 3
3
3. log9 36 log9 18 log9 24
4. log 4 20 log 4 5 log 4 8
5. log3 45 log3 5
6. log2 5 log2 40
7. log 5 10 log 5
25
2
For problems 9 - 14, given that log3 x
9. log 3 2x
11. log 3 (4 x 2 )
2
13. log 3 (9 x y )
8. log4 40 log4 48 log4 15
2 and log3 y
5 , evaluate each logarithm.
2
10. log 3
x
12. log 3 ( xy )
3x 2
14. log( 3 )
y
Name_______________________________________Date__________________
For problems 15 - 20, solve and check.
15. 2log x log 32 log 2
16. 2log x log 3 log 27
17. log 4 ( x 2) log 4 ( x 1) 1
18. log 2 ( x 5) log 2 ( x 2)
2
19. log 2 x log 2 ( x 2) 3
20. log 6 ( x 1) log 6 ( x 4)
2
21. 2log m 3log m 10
22. log 3 x 2 log 3 2 x
23. log 3 s
24. log( x 2) log( x 1) 1 0
log 3 ( s 2) 1
25. log 7 ( x 4) 3 log 7 ( x 2)
2
26. log 2 (2m 4) log 2 (m 1) 3
For problems 27 - 30, use the properties of logarithms, including change the base (to base 10), and simplify, if
possible, to lowest terms.
27. log 3 17
28. log 7 48
29. log 8 64
30. log 4 100