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

IB SL Math Portfolio- Logarithm Bases

Extracts from this document...


IB Math SL Portfolio Type 1 General Introduction: In its simplest terms, a logarithm is an exponent. It is an exponent needed to produce a given number from a specific base. It is written in the form loggh=j, which denotes gh=j (g to the power of h equals j). LOGARITHM BASES Consider the following sequences. Write the next two terms of each sequence. log28, log48 , log88, log168, log328, ... log648, log1288, ... log381, log981, log2781, log8181, ... log24381, log72981, ... log525, log2525, log12525, log62525, ... log3,12525, log15,62525, ... : : : logmmk, logm^2mk, logm^3mk, logm^4mk, ... logm^5mk, logm^6mk , ... Find an expression for the nth term of each sequence. Write your expressions in the form p/q, where p and q are integers. Justify your answers using technology. The first sequence can be otherwise written: log2^123, log2^223 , log2^323, log2^423, log2^523, ... Here, I noticed a pattern: the base of each logarithm is 2n. ...read more.


The same rules apply for the fourth and final sequence. logm^1mk, logm^2mk, logm^3mk, logm^4mk, ... logm^1mk = k/1 logm^2 mk = k/2 logm^3 mk = k/3 logm^4 mk = k/4 : : logm^n mk = k/n The nth term of the fourth sequence can expressed as k/n. Now, calculate the following, giving your answers in the form p/q, where p and q are both integers. log464, log864, log3264 3/1, 2/1, 6/5 log749, log4949, log34349 2/1, 2/2, 2/3 log1/5125, log1/125125, log1/625125 3/-1, 3/-3, 3/-4 log8512, log2512, log16512 3/1, 9/1, 9/4 Describe how to obtain the third answer in each row from the first two answers. First, I took the lowest prime base possible of each. log2^264, log2^364, log2^564 log7^149, log7^249, log7^349 log(1/5)^1125, log(1/5)^3125, log(1/5)^4125 log2^3512, log2^1512, log2^4512 In doing this, I noticed a pattern : the exponent of the base of the answer in the third column is simply the sum of the exponents of the bases in the first two columns when each base is in its lowest prime form. ...read more.


If a or b were equal to one, then c and d would be rendered undefined. (For example, if a=1 and x=3, the given statement logax=c would be undefined for c because there is no exponent that can be raised to make one equal three. One to any power always equals one.) This is the same for b. If it were equal to one, d would be undefined. They cannot be negative, as this does not work with the equations. The variable c cannot equal negative d, as this would yield a zero in the denominator of the equation, which would make it undefined. Explain how you arrived at your general statement. I explained it step by step above, but generally I just used my knowledge of logarithm and exponent rules to mold and simplify the information I was given. For example, I knew that logax=c was the same as writing x= ac, a point I explained in the brief introduction, which helped me not only with this portion but the portfolio in its entirety. ?? ?? ?? ?? ...read more.

The above preview is unformatted text

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. Math IB SL BMI Portfolio

    the data points in those areas, therefore the b value should be changed from ?/15 to ?/14. The number ?/14 was chosen because reducing the denominator's value by 1 will increase the b value by a slight amount, and an increased b value will shorten period and compress the graph

  2. Logarithm Bases Math IA

    If the following two statements are true, Then this next statement must also be true, Therefore, the statements above will be used to prove that within this next statement: This investigation aimed to prove that this equation: is true for all similar logarithmic sequences.

  1. Extended Essay- Math

    "W�(c)eV'�v�k���>[\L�ZJ�A!Q@it�D���@"6d�B���MO�7M�o�8%g�...3eH/ �s1/4����M� x�);-�˱E�@�S",Z(c)^Z�?);ȡ�MZD��^T�(c)^��F��A7m��2�R"~D�ß���:�Ѭ��d=2O��ۤ7�(c)'S��'|���OD~z ��o���NGy��ڨ��["8�?|koqc�"3/4�p����U(r)�)"911/4DN�*�mC=� ���� 8���G��� �1/2k(c)M ������G�X�w��I��U��;��� ��/�"�1/4� ��x��{�Nj#��2$ ��5Z�3�M�����˳�52����(c)...Ï��!�?DNr5�:�i�+ �"��#-M�{ O0�K��ts�2W��O-hk�|{�Ç�Luh��b1/4 ���d�S" �J_���H���4K�O��Ì�&9m;"��j���� �t�x2+�8�3��'�.p��>�*W���...K�,+�= �K�������!Xs��<y(� c���Q������e��괣...m��i�}.�N�H+�"�m^��x>R���&�O-ZM7&�uj���-M��Z�G>sÕª*'�'O�g��c��1�M"��$�m��m��_��� j �-!<i�2a-��?'�G��!"o0'�v�?@�n>��oxÛ��...*���(tm)�%�(tm)FF���-=d$��e.!'(c)�cÒ�'��y�_��3���e �O�z�í§]<���kX��v�@n�'��1/4�q��)C�5��8�sl"\$�~�,��?�po\�g�� �x�:Lg(r)$� ��)y�B$���F�5E���4@J$�n��?�p�Y���]G'Ë¥ckÛ@�8+4��C�Hñ��FD >���ADD"�-eN�!� 4v�W9�sQ�t� �...N�I E"X G3/4�'��g�e��.��>'��p-7mj7�'�=2�ج���GҰ�sÛa) Û¸o��EiG5�N...7...�p @���P�0�W"%�"n"RB'��"P�7�r�-�.b�@ p�$����#}���do\��w�lB�,�"� �*�ztk_�3��9��HO�6a�~.� -|{]�=�$dAV� ���HwjX��L�x�I�b�� �0��Z �'F�ʰ-�F��W6Þ��\����D�K�"�����o��ï¥G�?Q��M�..."�)�7��~5�G#�ɿ!Q'~.�fH �K����O��I"���q� ����9F�q��J��B����,?�a3/4E�%>#�DÈ·V~Q�%�@ ztEO�(-���� (r)q�p�[�'>)+�� �ۺ`~ "�mg�B��${���'���|Cd1/4'�46��"!3��oE.(tm)���~��3Ð"(c)�M��'8���"�1�� ^B-;"�à¯ï¿½1/4��3*I3�F��N�m�#�S7�b�j�E�!

  2. Artificial Intelligence &amp; Math

    of arrests and decrease the amount of crime that is committed through the Internet. Hackers, cyber terrorists and white-collar criminals will be under threat by the system as their every keystroke and mouse click is monitored for clues to their criminal activities.

  1. IB Math SL Portfolio Type 2 Population in China

    is not a realistic representation therefore I will continue with the Researcherâs model. The Researcherâs model shows a constant rise in the population. Final model Original Data I now graph the new set of data: X Y 1950 554.8 1955 609 1960 657.5 1965 729.2 1970 830.7 1975 927.8 1980

  2. Gold Medal heights IB IA- score 15

    With specific reference to the last data point, (1980, 236) the regression model does not accurately represent the data. In the same case, the refined model is able to represents this point since it has greater amplitude. Another difference between the two model function is the difference of horizontal stretch.

  1. IB Math Methods SL: Internal Assessment on Gold Medal Heights

    Let us now plot the table values for the quintic function so we can compare the values between all three tables. Using the Autograph table plotting apparatus; a table of data has been generated for the quintic function (see Appendix, figure 3).

  2. SL Math IA: Fishing Rods

    Point: (1,10) (3, 38) (8,149) A = , X = , B = The equation is: = Next, by using our GDC, we can determine the inverse of matrix A, and multiply both sides by it. Therefore we have determined that the quadratic equations given the points {(1,10), (3,38), (8,149)} is .

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