• 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...

Introduction

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.

Middle

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.

Conclusion

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. 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�!

  1. 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.

  2. Artificial Intelligence &amp; Math

    Either the possible threat is dismissed or acted upon defensively by police, leading to a decrease in successful cyber crimes. IT concepts well described and some developments; not enough detail, particularly of developments for explanation, and certainly no analysis. The Impact of the Issue The legislature will increase the number

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

    function and the linear function (reproduced below): Information Table 2 (Table of values from linear equation y = 1.02x + 187) Years Elapsed (t) 0 4 8* 12* 16 20 24 28 32 36 40 44 48 Height in cm (h)

  1. Gold Medal heights IB IA- score 15

    Algebraic derived function : Converted to approx. Degrees : Regression by Graphmatica: h = 12.871 sin (0.0818t + 3.0456) + 213.5766 There are many similarities, solely based on the visual representation of the two model functions. Both models begin with a negative slope and hit a minimum point relatively the same area.

  2. SL Math IA: Fishing Rods

    Therefore we have finally determined our quadratic function to be: Rounded to 4 sig figs, too maintain precision, while keeping the numbers manageable. Data points using quadratic function Guide Number (from tip) 1 2 3 4 5 6 7 8 Quadratic values Distance from Tip (cm)

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