1140 L21 - y = log 2 x . Properties of the graph of f ( x )...

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Lecture 21: Section 3.2 Logarithmic Functions Recall that exponential function f ( x ) = a x is one-to-one, and therefore it has an inverse function. This inverse function is called the logarithmic function with base a Def. The logarithmic function with base a is written as f ( x ) = log a x , where x > 0, a > 0 and a 6 = 1 and is de±ned by the relationship y = log a x if and only if ex. Write in exponential form: 1) log 3 ± 1 9 ² = ± 2 2) log e (3 x + 1) = 2 ex. Write in logarithmic form: 4 1 : 5 = 8
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ex. Evaluate: 1) log 2 64 = 2) log 3 1 = 3) log 3 3 = 4) log 10 ± 1 1000 ² = 5) log 16 4 = 6) log 2 ( ± 1) = 7) log 2 0 =
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Properties of Logarithms 1. Recall: If y = log a x , then x = That is, x > 0. 2. log a 1 = 3. log a a = 4. Inverse Properties: log a a x = for all real number x a log a x = for x > 0 5. One-to-One Properties: If log a x = log a y , then ex. Using inverse property, evaluate: 1) 2 log 2 3 ± = 2) log 5 1 5 = ex. Using 1-to-1 property, solve log 2 ( x ± 3) = log 2 9
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Graphs of Logarithmic Functions ex. Sketch y = 2 x and
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Unformatted text preview: y = log 2 x . Properties of the graph of f ( x ) = log a x f ( x ) = log a x f ± 1 ( x ) = a x 1. Domain: 2. Range: 3. Intercept: 4. Asymptote: 5. increasing if decreasing if 6. points on the graph ex. Graph f ( x ) = log 3 ( x + 1) The Natural Logarithmic Function y = log e x = ln x if and only if Note the following: ln 1 = ln e = e ln x = ln( e x ) = If ln x = ln y , then ex. Evaluate: 1) e ln(2 x +3) = 2) ln ± 1 e ² = ex. Solve: ln( x 2 ± x ) = ln 6 ex. Graph and ±nd the domain and vertical asymptote of f ( x ): 1) f ( x ) = ln x 2) f ( x ) = ln( x ± 2) + 1 Practice f ( x ) = ln( ± x ) + 2 Common Logarithm Function y = log 10 x = log x if and only if ex. Evaluate: log 1 = log 10 = log 10000 = log 1 p 10 =...
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L21 - y = log 2 x . Properties of the graph of f ( x )...

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