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3.1 Concept Prep Assignment: Introduction to Logarithms

Try It!

With your small group, using your graphing calculators:

1. Go to TBLSET (2^ND WINDOW).   Let TblStart = 1;  Tbl = 1; Indpnt:  Ask; and Depend:  Auto.

2. Go to the Y= menu and in Y1= type in “log(x).”

3. Go to the TABLE menu (2^nd GRAPH) and type in arbitrary values for x.  The values for log(x) will appear in the output column (Y1).

4. Study the table and try to figure out what the “log” function means.  Make a list of conjectures on your own paper, noting any patterns and relationships you find.  (You might want to write your table on paper, too, since this feature of the calculator will only let you look at 7 rows at a time.) 

Class Discussion

5. Now return to the TBLSET (2^ND WINDOW) menu and Let TblStart = 0;  Tbl = 100; Indpnt:  Auto; and Depend:  Auto.

6. Study the new table and jot down any new relationships in the outputs that you see.

7. For what values is Y=log(x) undefined?  Why do you think this is so?

8. In the table below, what is the relationship between the numbers in the columns?

1

2

2

4

3

8

4

16

5

32

6

64

7

128

8

256

9

512

10

1024

1

3

2

9

3

27

4

81

5

243

6

729

7

2187

8

6561

9

19683

10

59049

1

10

2

100

3

1000

4

10000

5

100000

6

1000000

7

10000000

8

1E+08

9

1E+09

10

1E+10

11. Discussion:  Can any number be expressed as a power of 10 ?  Use the graph of  below to support your argument.