Math IA Logarithm bases

Logarithm Bases

Consider the following sequences. Write down the next two terms of each sequence.

Log 2 8 , Log 4 8 , Log 8 8 , Log 16 8 , Log 32 8 , Log 64 8 , Log 128 8

Log 3 81 , Log 9 81 , Log 27 81 , Log 81 81 , Log 243 81 , Log 729 81

Log 5 25 , Log 25 25, Log 125 25 , Log 625 25, Log 3125 25 , Log 15625 25

Find an expression for the nth term of each sequence. Write your expressions in the form P/Q.

Log 2 8 , Log 4 8 , Log 8 8 , Log 16 8 , Log 32 8 , Log 64 8 , Log 128 8

This sequence can be expressed 3/N. N being the nth term of the sequence.

1st Log 2 8 = 3                        3/1 = 3

2nd Log 4 8 = 1.5                                  3/2 = 1.5

3rd Log 8 8 = 1                        3/3 = 1

4th Log 16 8 = .75                        3/4 = .75

5th Log 32 8 = .6                        3/5 = .6

6th Log 64 8 = .5                        3/6 = .5

7th Log 128 8 = .43                        3/7 = .43

Find an expression for the nth term of each sequence. Write your expressions in the form P/Q.

Log 3 81 , Log 9 81 , Log 27 81 , Log 81 81 , Log 243 81 , Log 729 81

This sequence can be expressed 4/N. N being the nth term of the sequence.

1st Log 3 81 = 4                        4/1 = 1

2nd Log 9 81 = 2                        4/2 = 2

3rd Log 27 81 = 1.33                4/3 = 1.33

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