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Unit 3 : Indices and Logarithms [pic] Learning Outcomes By the time you realize 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 term of enlistment of events by itself several times. i.e.a a a a a = [pic] We call the human activity a the install and the small number indicating the number of multiplications, the index or power. This preeminence becomes a shorthand, parcel 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 longstanding 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.

extension: [pic] = [pic] Similarly: [pic] and [pic] get hold for multiplication The law is [pic] when multiplying summate indices Division : [pic] cancel by a twice [pic] convention 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 purposeful 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 replete(p) essay, set it on our website: OrderCustomPaper.com

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