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# Logarthimic Patterns

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Introduction

Shamit Prabhu

=-     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: Let and . Find the general statement that expresses , in terms of c and d.

The general statement that expresses 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. ab 1

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 and by using the change of base formula we get . The natural log of 1 is 0, thus this equation is undefined because the denominator is 0.

For example,

Conclusion Find and expression for the nth term of each sequence Write your expressions in the form ; where p,q . 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: = =3 = =4 = = This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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# Related International Baccalaureate Maths essays

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

Below will be two examples of sequences that follow this same pattern. Sequence #1 log6216 , log3216 , log18216 (6)(3) = 18 Sequence #2 log232 , log532 , log1032 (2)(5) = 10 Multiply the bases of the first and second logarithms to find the base of the third logarithms.

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

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