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Unit 3 : Indices and Logarithms [pic] acquire Outcomes By the time you realize completed this Unit, you should be commensurate to: [pic]show your understanding of the virtues 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 indication ? The idea of an list (or power) tog ups when we calculate a turn of events by itself several times. i.e.a a a a a = [pic] We crab the upshot a the stalk and the small weigh indicating the number of multiplications, the index or power. This notational system becomes a shorthand, helping us to bring out calculations of this material body without multiplication signs. However, the notation presently takes over and is applied to other forms that atomic number 18 no longer so easy to understand. We flip-flop the continue multiplication with a bingle operation - winning an index, or raising to a power. [pic] By investigating what happens during the divers(prenominal) operations of arithmetic, we back end derive the law of natures of indices.

Multiplication: [pic] = [pic] also: [pic] and [pic] get hold for multiplication The law is [pic] when multiplying add indices Division : [pic] repeal by a twice [pic] precept for division The law is [pic] when dividing subtract indices For prototype: [pic] [pic] but what is a negative power? [pic] Several points arise from these examples. 1. It is only meaningful to approve indices applied to the same home plate - 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 extremity to get a wide essay, set it on our website: Ordercustompaper.com

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