- Level: International Baccalaureate
- Subject: Maths
- Word count: 1209
The reasoning behind conducting this investigation is to identify patterns in logarithmic sequences. Furthermore, after identifying the patterns, one must produce a general statement expressing the general trend within the sequence.
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Introduction
International baccalaureate
Mathematics SL
Portfolio Type one
Logarithm bases
CANDIDATE NAME : Shilpi Singhvi
CANDIDATE NUMBER :
SCHOOL NAME : GANDHI MEMORIAL INT’L SCHOOL
SCHOOL CODE : 000902
SESSION : MAY 2010
Logarithm Bases
INTRODUCTION
The reasoning behind conducting this investigation is to identify patterns in logarithmic sequences. Furthermore, after identifying the patterns, one must produce a general statement expressing the general trend within the sequence. Once forming a general statement, one must be able to rewrite logarithms in the form of a fraction. This investigation tests the acquired knowledge of logarithms by testing the general statement using various values, forming limitations, and proving scopes. In addition, further investigation may be conducted through the use of graphs, tables of values, and charts.
This assignment is looking for a formula that will give the nthterm for the sequence.
This table gives the next two terms of each sequence.
nth | sequence(1) | sequence(2) | sequence(3) | sequence(4) |
1 | log8 | log81 | log25 | logm |
2 | log8 | log81 | log25 | logm |
3 | log8 | log81 | log25 | logm |
4 | log8 | log81 | log25 | logm |
5 | log8 | log81 | log25 | logm |
6 | log8 | log81 | log25 | log m |
7 | log8 |
Middle
Thus the nth term is where p is k and q is n.
Describing how we obtain log(64) from log(64) and log(64).
In order to obtain the answer of the third logarithm, the product of the first and second logarithms must be divided by the sum of the answers of the first and second logarithms.
log(x), log(x) log(x)
We use the formula:
logb =
log(x) = log4 = [1]
log(x) = log8 = [2]
Add [1] and [2]:
log4 + log8 = +
And we have:
log32 =
Therefore the formula we obtain:
log(x) =orlog(x) =
By replacing the value of x = 64 we get,
log(64) =
log(64) = 3 & log(64) = 2 (using GDC)
Thus, log(64) =
Describing how we obtain log(49) from log(49) and log(49).
Thus by using the above formula above:
log(x) =
log(49) =log(49) log(49)
log(49) + log(49)
Solving the equations,
log(49) = 1
log(49) = 2
Therefore,log(49) =
Describing how we obtain log (125) from log (125) and log (125).
Thus, by using the formula
log(x) =,
log (125) =
+
Solving the equations
log (125) & log (125) by change of base log
= -3= -1
Therefore,
Conclusion
Now by simplifying loga x= c and logb x = d by changing the base logs by the formula above and making loga x and logb x as the subject of the formula and substituting in the first part we get the general statement as .
2nd way:
We simplified the statement logab x by making the bases similar.
Now in the equations loga x= c and logb x = d we used the formula to make the bases similar i.e. and making loga x and logb x as the subject of the formula.
Then we substituted it in the simplified version of logab x . By substituting the values we get the general statement.
Through this general statement we can find out the value of the third term in a sequence when the first two terms are given.
Conclusion
In conclusion, after applying the given knowledge of logarithms, a general statement was formed to prove the validity of various sequences. Also through the use of technology, general statements were proven and theories were confirmed.
This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.
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