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

Logarthimic Patterns

Extracts from this document...

Introduction

                Shamit Prabhu

=-image11.pngimage11.pngimage11.pngimage00.pngimage01.png

Describe how to obtain the third answer in each row from the first two answers. Create two more examples that fit the pattern above.

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.

Two other examples that fit the pattern above:

image23.png

Let image08.png and image09.png. Find the general statement that expresses image24.png, in terms of c and d.

The general statement that expresses image24.png

...read more.

Middle

Scopes and/or limitations of a, b, and x

1. a > 0, b > 0

The base of a logarithmic equation has to be greater than zero thus, a has to be greater than 0 and b has to be greater than 0.

2. abimage04.png1

The base of a logarithmic equation cannot be one because any argument to the base 1 is undefined. If you take an equation such as image05.png and by using the change of base formula we get image06.png. The natural log of 1 is 0, thus this equation is undefined because the denominator is 0.

For example,

...read more.

Conclusion

image13.png

Find and expression for the nth term of each sequence Write your expressions in the form image14.png ; where p,qimage15.png. Justify your using technology.

Using a TI-84 calculator we verified the answers we got by taking each logarithmic expression and by using the change of base formula. By doing so we took the natural log of the argument and divided it by the natural log of the base. For example:

image16.png=image17.png=3                                                                        

image18.png=image19.png=4

image20.png=image21.png=image22.png

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

    First Sequence (4)(8) = 32 Second Sequence (7)(49) = 343 Third Sequence (1/5)(1/125) = 1/625 Fourth Sequence (8)(2) = 16 Values found using the base numbers of the first and second logarithms. Different values can be used for the nth terms in a sequence.

  2. The reasoning behind conducting this investigation is to identify patterns in logarithmic sequences. Furthermore, ...

    Justify using technology: In this manner, I created a formula to find the numerical equivalence for the nth term of the sequence in the form, where both p and q are integers. 2. log81 = 4 log81 = 1 or log81 = 2 or log81 = 0.8 or log81 =

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