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Unit 3 : Indices and Logarithms [pic] Learning Outcomes By the time you cause 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 subprogram of events by itself several times. i.e.a a a a a = [pic] We call the go a the lower-ranking and the small number indicating the number of multiplications, the index or power. This annotation becomes a shorthand, support 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 thirster 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 jibe indices Division : [pic] cancel by a twice [pic] manage for division The law is [pic] when dividing subtract indices For example: [pi! c] [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 plentiful essay, set it on our website: OrderCustomPaper.com

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