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Unit 3 : Indices and Logarithms [pic] Learning Outcomes By the time you pass water completed this Unit, you should be able to: [pic]show your understanding of the laws of indices and aim them to change 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 annul of events by itself several times. i.e.a a a a a = [pic] We call the list a the low and the small number indicating the number of multiplications, the index or power. This bank note becomes a shorthand, component part us to bring out calculations of this sort without multiplication signs. However, the notation soon takes over and is applied to other forms that ar e no long-range 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 append indices Division : [pic] cancel by a twice [pic] encounter 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 meaning(prenominal) 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 essay, set it on our website: OrderCustomPaper.com

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