Logarithm Base
IB Math SL
Type I Portfolio
Lisa Phommaseng
Logarithm Base
Consider the given sequences:
Log28, log48, log88, log 168, log328,…
Log381, log981, log 2781, log8181,…
Log525, log2525, log12525, log62525,…
:
:
:
,…
For the first sequence Log28, log48, log88, log 168, log328,… you are to find the next two terms of each of the sequences you would have to determine the pattern. As we can see, the value of the bases, 2,4,8,16,32 are increasing by squares of 2 (ex: 22= 4, 23=8, 24=16 etc.,). The two terms following log328 will be log648 and log1288. To find the expression for the nth term of each sequence, you would have to write the expression in the form of . First you would find log28 to begin to look for a pattern. A formula that could be useful to solve this would be logbx = . The variable b would be the base, x would be the number of the logarithm. Saying that log28 = x, we are able to determine that x is 3 because 23 equals 8. The same would follow for the next terms : log48= x, 8 is equivalent to 23 and the base of 4 is equivalent to 22 (Log28 =). So, to that term would be . You would continue on with the next and you would notice that the pattern is 3 over whatever the number that follows. Now we see that the nth term of this sequence is an=. The next sequence Log381, log981, log 2781, log8181,…you would determine the following two terms as the one above. A we can see the terms are squaring as well. The bases are increasing as so : 31=3, 32=9, 33= 27, 34=81, and so forth. We can determine that the following terms are going to be log24381 and log72981. You would also find the expression for the nth term the same way. Using the formula logbx = we are able to see that log381 = x and x = 34 or 4. Following that log981 is equal to for log981 = . The nth term of this sequence is an=. So, the following two terms of the last two sequences would be log312525 and log1562525 for the sequence Log525, log2525, log12525, log62525,…...
...found that some little error exist between real data and the function we got. Observe the time of the data, it is clear that there are large difference between the data, the scale of time is from 0.01 to 30, which is that uniformly distribute. So, logarithm axis is considered to scale the time. We can get new data table as follows:
Time (min)  Log Time (min)  Ln Time (min)  +Gx (g) 
0.01  2  4.61  35 
0.03  1.52  3.51  28 
0.1  1  2.3  20 
0.3 ...
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Height (cm)
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Notation and Terminology
Check for the following:
• I did not use calculator notation. (I didn’t include things like ‘x^2’ for or Sn for Sn)
• I used appropriate mathematical vocabulary.
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Check for the following:
• The reader will not need to refer to the list of questions in order to understand my work.
• My responses are not numbered.
• I have an introduction, conclusion,...
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Personal Statement
I am a passionate, persistent individual who wills to become a bachelor in British Law, in order to, further on, exert the profession of a lawyer. I am and have always been deeply interested in the principles of justice, which I try to put into action in my everyday life.
My intention on entering a Law School is acquiring a deeper knowledge on the subject which has always been my main interest, both in my social and in my personal...
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