Math 112 4.4 Notes

# Math 112 4.4 Notes - evaluate 9 8 log b Example 9 Given log...

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Section 4.4 Properties of Logarithms: 1. Product Rule For M, N > 0 ) ( log ) ( log ) * ( log N M N M a a a + = 2. Power Rule For M > 0 ) ( log * ) ( log M p M a p a = 3. Quotient Rule For M, N > 0 ) ( log ) ( log log N M N M a a a - = Example 1: Write ln(c*d) as a sum of logarithms Example 2: Simplify log p (x -6 )

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Example 3: Write d D log as a difference of logs. Example 4: Simplify z y x 9 7 * ln
Example 5: Simplify 4 2 3 * log z y x Example 6: Simplify log(x 2 +3x-18) – log(x 2 -36)

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Example 7: Write ) log( 4 ) log( 2 ) log( 2 1 z y x - + as a single log Example 8: Given log b (8) = 2.079 and log b (9) = 2.197,

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Unformatted text preview: evaluate 9 8 log b Example 9: Given log a (5) = .699 and log a (2) = .301, evaluate log a (125) Converting logarithm of a base to a power: For any base a and any x, 1. log a (a x ) = x 2. x a x a = ) ( log Example 1: Simplify ( 29 4 log t t Example 2: Simplify ) log( 10 y z + Example 3: Simplify ) ( log p p Example 4: Convert e-3 = r to a logarithm. (Recall that e x and ln(x) are inverse functions)...
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## This note was uploaded on 04/07/2008 for the course MATH 112 taught by Professor Taylor during the Spring '08 term at Alabama.

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Math 112 4.4 Notes - evaluate 9 8 log b Example 9 Given log...

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