Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write each equation in logarithmic form.

12. 49 = 7 2 49 equals , 7 squared
13. 10 3 = 1000 10 cubed , equals , 1000
14. 625 = 5 4 625 equals , 5 to the fourth
15. 1 10 = 10 − 1 1 tenth , equals , 10 super negative 1 end super
16. 8 2 = 64 8 squared , equals 64
17. 4 = ( 1 2 ) − 2 4 equals . open , 1 half , close super negative 2 end super
18. ( 1 3 ) 3 = 1 27 open , 1 third , close cubed . equals , 1 twenty seventh
19. 10 − 2 = 0.01 10 , negative squared , equals , 0.01

See Problem 2.

Evaluate each logarithm.

20. log 2 16 log base 2 , 16
21. log 4 2 log base 4 , 2
22. log 8 8 log base 8 , 8
23. log 4 8 log base 4 , 8
24. log 2 8 log base 2 , 8
25. log 49 7 log base 49 , 7
26. log 5 ( − 25 ) log base 5 , open negative 25 close
27. log 3 9 log base 3 , 9
28. log 2 5 log base 2 , 5
29. log 1 2 1 2 log base 1 half . 1 half
30. log 10,000
31. log 5 125 log base 5 , 125

See Problem 3.

Seismology In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.

32. magnitude 7.7 in San Francisco, California, in 1906
33. magnitude 9.5 in Valdivia, Chile, in 1960
34. magnitude 3.2 in Charlottesville, Virginia, in 2001
35. magnitude 6.9 in Kobe, Japan, in 1995

See Problem 4.

Graph each function on the same set of axes.

36. y = log 2 x y equals , log base 2 , x
37. y = 2 x y equals , 2 to the x
38. y = log 1 2 x y equals . log base 1 half . x
39. y = ( 1 2 ) x y equals . open , 1 half , close to the x

See Problem 5.

Describe how the graph of each function compares with the graph of the parent function, y = log b x . y equals , log base b , x .

40. y = log 5 x + 1 y equals , log base 5 , x plus 1
41. y = log 7 ( x − 2 ) y equals , log base 7 , open x minus 2 close
42. y = log 3 ( x − 5 ) + 3 y equals , log base 3 , open x minus 5 close plus 3
43. y = log 4 ( x + 2 ) − 1 y equals , log base 4 , open x plus 2 close minus 1

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