G1notes - Supplementary Course Module G: Exponentials and...

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Supplementary Course Module G: Exponentials and Logarithms Exponential and Logarithmic Operations Consider the seemingly innocent enough numerical expression, 3 2 . There are two different ways of looking at this expression, depending on where we start! 1. If we start with the 3 , the expression translates to " 3 to the power of 2 " This is an example of a power operation and can be broken down as follows: 3 |{z} given value % 2 o operation = 9 |{z} answer That is, given the value 3 and applying the operation of "to the power of 2 ", we obtain the answer 9 . An opposite (or inverse) operation should take an answer and produce the original given value. We would use operation q 9 |{z} orig. answer = 3 |{z} orig. given 3 2 = 9; p 9 = 3 If we replace the given value of 3 with the variable x , we have that x 2 (power of 2 ) and p x (square root) are opposite operations. In general, if n is a non-zero positive integer, x n (the n th power) and n p x (the n th root) are opposites. This is probably the more common way of looking at the expression 3 2 . But what if we start at the 2 ? 2. If we start with the 2 , the expression translates to " 2 applied to the base of 3 " and the direction of the operation arrow changes direction: 2 g given value 3 . o operation = 9 |{z} answer That is, given the value 2 and applying the operation of "to the base of 3 ", we obtain the answer 9 the exponential operation. Looking at the opposite operation, this time we need to do something to the 9 in order to obtain the original given value of 2 . We know the base of the exponential operation was 3 , thus, we apply a logarithmic operation, 3 ": log 3 |{z} operation 9 |{z} orig. answer
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This note was uploaded on 11/25/2010 for the course MATH MA110 taught by Professor Hu during the Fall '10 term at Wilfred Laurier University .

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G1notes - Supplementary Course Module G: Exponentials and...

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