• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Math Portfolio type I Logarithm Bases

Extracts from this document...


Lukasz Weclas

Mathematics Standard Level

Portfolio Assignment Type II

Logarithm bases

Lukasz Weclas

        December 2009

Table of Contents

Table of Contents                                                                        02

Introduction                                                                                 03

Write down the next two terms of each sequence                                        03

Find an expression for the nthterm of each sequence and write in form image00.png                04

Calculate the value of given logarithms                                                 06

Describe how to obtain the third answer in each row from the first two answers        08

Create two more examples that fit the pattern                                        08

Find the general statement that expresses logabx                                        09

Test the validity of your general statement using other values of a, b and x        10

Discuss the scope and limitations of a, b and x                                        11

Explain how you arrived at your general statement                                        11

Technology used                                                                        12

Bibliography                                                                                12


        Logarithm is defined as the exponent that indicates the power to which a base number is raised to produce a given number[1]. In this assignment I shall attempt to investigate the characteristics of sequences of logarithms. As a conclusion, I will try to find the general statement and finally the range and limitations of a, b and x will be considered.

...read more.


image44.png. The answers will be justified with the use of GDC Casio CFX-9850GB PLUS.

A: image46.png

Now I substitute n for any given number, for example 15. Let n=15


To justify my answer, I will use my GDC to check if it is correct


The answer is the same, therefore it is correct.

B: image02.png

Now I substitute n for any given number, for example 12. Let n=16


To justify my answer, I will use my GDC to check if it is correct

The answer is the same, therefore it is correct.

C: image05.png

Now I substitute n for any given number, for example 8. Let n=8


To justify my answer, I will use my GDC to check if it is correct


The answer is the same, therefore it is correct.


Conducting the same process is not possible in case of sequence X, but the three equations above should prove that calculation would be possible if k, n image09.pngimage10.png.

Calculate the value of given logarithms

The next task is to calculate the following sequences given in the assignment, then give my answers in the form image00.png, where p, q image09.pngimage10.png:


...read more.


a, b ≠ 1. The best method to check the validity of my general statement is to use different values of a, b and x.
  1. Let a = 3, b = 9 and x = 729


Next it is necessary to calculate to value of image38.png

Later the use of formula image40.png

In this example the statement is true, because image41.png

  1. Let a = 4, b = 6 and x = 1


By the definition it is known that logwq = j, then q = wj, therefore if q=1 then j = 0. In that case log41 = 0, log61 = 0 and log241 = 0. As a conclusion, the argument of a logartihm has to be different from 1.

Discuss the scope and limitations of a, b and x

        For statement image43.png to be true two conditions have to be met:

1) a, b, x > 0

2) a, b ≠ 1

Explain how you arrived at your general statement

        I arrived at my general statement when I was thinking how to write the expression for nth of each sequence in form image00.png. Then I used the two formulas image39.png and image44.png. The series of calculations (and final one presented below) lead to the general statement.


Technology used

  1. For all the calculations:


  1. For all the graphic presentation:

Microsoft Office Word 2007

MathType v. 6.5c


[1] http://m-w.com/dictionary/logarithm

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    ��Ө�2:#�(tm)�V�B��Q:"L�"1�I�[0�0�%�b�e�e1/2Â���������]�x �)|N"Y,S|V�V�E�N�O���-R��i�~Õ·jk���Z'��:ƺ�z-�� ��F%�&]���^��Y�Z��l�m�v)�i�:X8�:98;"�����"{xx�����������@��5��W � � b ��S�"1/4 }vY�""��D'�Pb �8�3/4�&"&F&Y& %o�<Km�{0�']-� Y[׳ �����0�����-:|P;�5o3}X�H�Q�cW�o�K��-'/U(S*W(r)P(c)T9(c)Z�y��t�(tm)��5,��1/4�"Χ��6o�1/4p(r)(c)�����-�K��\��6�&�-�Q����ì­n�[ =.1/2...}s���w-�};�x�@d��p죰��j�1/4c4ckO��>���k���[/z'"_�1/4:�:������'w���+g�}�?�<>����"�y���;_j��] Y�]V�*�Mb��{����o686ݶj��w�'%:��>@bP$�s���2* �}#����dq_�}"*�4�?��'Î�-!�1�\�4��U�Í1/2���Û�0�0?I�^�ÐQ�D,A1/4N��7iqYe9 y %E %^eH�� �[ jtj6hUh�����ַ504T3'56�4e0Ú��/Z�XNX Yw�\���Ud-c�@q�s�u-rawŸ.�1/2t��g�W�-/oi ��+�^�Ú���A6�rTF�×��mae��n'�Q��[1E��q*��"s��I&����)WR3�ڦq�}L��8''�m�x��~�\�R E� q�"� �l|?�tl��Z(r)��"x�Z(c)q(tm)]�� Ê"iU N�>y�Ù�Ñ�su����[^4n5 4�\ n9r(c)��-"*��>n'u�tR"ʯ?��ݭr+�����m�~��"����æ"-z g?jy6�S~�4g1/4�Y�Ä4"r/�^%�>�����;...�Wg-g���k>3/4Y����_�K _eV�"4k��O׷�Û�i`�Ԧ��>"...� ��4��E'P��8t!FÓ��'q�� �4|4k�'��st��... G �L��XY_��q�9e�L�)<{yK�.� <��,1/4,��dM�}�$�IyH��@2���r��- � "��Ju��*Ϊ�j��"z�F���-�֦��N�n���>������9�tcYS��K�k�,|,U��VSÖ­6y�^H���=�or�tttq��<�R���Nt��;��Ü����>V6ʴ�E��Æ�� �`-*�:R�&��'iE��>c���Ë×_OhO�M'M�O(r)M�N�L}�� �<N��H�4���ZÏ�7�syenÎ�.y��D�I�+�_-�]�x��X���Â��b$-(�.�.�*�� V��t��<e}��L�٪ê/�X���[�;4�7�3/4��t�y1/2��R��7W�(r)%���;;˺&o� �3/4����w"�k ��� �1/2��O�$fO��<-�{�2~p��y����(tm)S6���:_1/40��|���-v��*�Lp)�Q���#��6v$�4�Q �Q��g���ޱÔ$z`'�a...BG ����Z�71/4(r)���(N"*u Õz�&�U��t'zÂ1��#U�-k�M�^���qÞ¸S��xA|0�~"`M8C�NcG�L$#����gIDRi�Ξ(r)-^'3/4-���#�q?&g3a����YDX(r)��N�E���k9�8�s-�'�zÊ�#��'��Ïo"�K EPW#�H��H���Y�x�D�d�T���������1/4(r)��b��>$�*��(c)}���4�J�n�y�ǡ�jPn��X�$��9�E�� "R�}�m��]��B�(c)

  2. IB SL Math Portfolio- Logarithm Bases

    One could also use the "solver" function on a GDC calculator to check their math by simply pressing the "math" key, then pressing "solve". The original statement can be written 2x=8, but in order to input this into the solver function, it needs to be set to zero.

  1. Logarithm Bases - 3 sequences and their expression in the mth term has been ...

    terms in the sequence were also verified by using the TI-83 where: U2: log25 25 (1) U3: = log12525 (0.66) U4: : = log62525 (0.5) U5: : = log312525 (0.4) U6: : = log1562525 (0.33) L.H.S = R.H.S. Hence, Verified that is the general expression for the 3rd row of the given sequence in the form .

  2. Ib math HL portfolio parabola investigation

    Now for a cubic equation, we have 6 roots when it intersects with two straight lines. These six roots are X1, X2, X3, X4, X5, and X6. We can express any cubic equation in its factored form as: = a(x r1)

  1. In this investigation I will be examining logarithms and their bases. The purpose of ...

    log164096 log44096 log644096 = 3 = 6 2. log121728 log61728 log721728 = 3 = 4.16 3. log27729 log3729 log81729 =2 = 6 4. log2401 log2401 log2401 = -2 = -4 5. log20736 log20736 log20736 = -2 = -4 After testing the validity of the general statement, I realized that the statement does not work for all numbers.

  2. Math Portfolio Type II Gold Medal heights

    The sin or cosine function for that matter are unsuited, as they are only able to depict discrepancies that occur with a regular pattern. The function of a logarithm seems to provide the most suitable choice. It shows a slow steady slope, that decreases as the x-values grow.

  1. Logarithms. In this investigation, the use of the properties of ...

    log27 change multiplier to exponent log8 / log64 log8 / log128 expand exponential log648 log1288 change the base to rewrite logarithm In the second, third, and fourth sequences, the setup of the terms is very similar to that of the first sequence where the base of the logarithm changes but not the .

  2. Logarithm Bases Math IA

    bases of the first and second log, you get the base of the third log, for example: 4 x 8 = 32.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work