Logarithm Active Practice Level 2
Special Properties of Logarithms: Simplify this set of problems and summarize what you observe in your notes!!!
Assume “a” and “b” are any positive number other than 1. Solve for y and switching it into an exponential might help.
A. log x x a = y
B. log b b = y
C. log b 1 = y
D. log b 0 = y
E. log1 a = y
F. b logb x = y
Practice Problems: Try to evaluate each expression without a calculator.
Change each equation to logarithmic form.
1. 52 = 25
2. 2 5 = 32
3. 3−2 =
1
9
Change each equation to exponential form.
4. log 2 128 = 7
5. log 4 8 =
3
2
6. log 0.01 = −2
Evaluate each expression without a calculator.
2 log2 8
7. log 64 8
8. log 7 73
9.
10. log3 3
11. log 7 1
12. log1 6
13. log 5 0
14. log 6 36
15. log 4 2
16. log3 x = 2
17. log3 x = −4
18. log 4 x =
19. log3 (−9 ) = x
20. log3 1 = x
21. log 7 79 = x
22. log x 2 = 0
23. log x 64 =
( )
1
2
!1$
& = −6
" 64 %
3
4
24. log x #
25. log3 32
26. log 5 125
27. log15 15
28. log36 6
29. log 7 1
log 16
30. 4 4
31. log 7 0
32. log1 9
33. log 2
1
8
Challenge Problems
216
#What.) log 25
=
125
36
#Fallingoffthelog.) 5
log 5 (12−x )
=9
#WhatTheFunction(WTF).)
( 3)
27
x+2
x
= 3− x
2