ss_4_4

ss_4_4 - Section 4.4. Properties of Logarithms Properties...

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Section 4.4. Properties of Logarithms Properties of Logarithms: log a 1=0 log a a =1 log a M r = r log a M log a a r = r a log a x = x log a M =log a N implies M = N log a ( MN )=log a M +log a N log a ( M N a M - log a N The following examples illustrate the above rules. Example. log ( x ( x +1) 2 ) x +log( x 2 = 1 2 log x +2log( x Example. log x ( x +1) 2 x - log ( x 2 = 1 2 log x - 2log( x Example. log 3 2 - 3log5 =log3 2 - log 5 3 3 2 5 3 9 125 Example. Suppose y =3 x 2 ,then ln y =ln3 x 2 =ln x 2 +ln3 =2ln x Interesting observation: In the previous example, y was a power function of x (i.e. y x 2 ), and this implied that ln y was a linear function of ln x , i.e., y x 2 implied that ln y x +ln3. The example illustrates the following general rule: 1
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y = ax b if and only if ln y = b ln x +ln a The above implies that if a plot of ln x against ln y , for some set of data, is a straight line, then one would expect y to be a power function of x for that set of data.
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ss_4_4 - Section 4.4. Properties of Logarithms Properties...

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