Adds

Unit 3 : Indices and Logarithms

[pic] Learning Outcomes

By the time you wee completed this Unit, you should be able to:

[pic]show your understanding of the laws of indices and aim them to
simplify expressions and transpose formulae

[pic]explain the rules of logarithms and how to use them


[pic]solve equations involving indices or logs, and move from one
to the another(prenominal)

[pic]manipulate formulae containing indices or logs.




What is an indicant ?

The idea of an list (or power) arises when we multiply a turn of events by itself several times.

i.e.a a a a a = [pic]


We call the number a the base and the small number indicating the number of multiplications, the index or power. This notation becomes a shorthand, helping us to bring out calculations of this sort without multiplication signs. However, the notation soon takes over and is applied to other forms that are no longer so easy to understand. We flip-flop the continued multiplication with a single operation - winning an index, or raising to a power.

[pic]


By investigating what happens during the divers(prenominal) operations of arithmetic, we can derive the laws of indices.





Multiplication: [pic]
= [pic]

Similarly: [pic]

and [pic]


get hold for multiplication

The law is [pic] when multiplying add indices



Division : [pic] cancel by a twice

[pic]


Rule for division
The law is [pic] when dividing subtract indices



For example: [pic]

[pic] but what is a negative power?
[pic]


Several points arise from these examples.

1. It is only meaningful to combine indices applied to the same base - hence
the powers of base b and c are subtracted separately.

2. A number or earn without a power is assigned the power of 1
i.e.c = [pic]
3. victimization the division law we can end up with both negative powers...If you want to get a full essay, set it on our website: Ordercustompaper.com



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