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14209an2.17-20

14209an2.17-20 - c Kendra Kilmer Section 2.5 Logarithmic...

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c circlecopyrt Kendra Kilmer January 20, 2009 Section 2.5 - Logarithmic Functions Definition: A function f is said to be if each range value corresponds to exactly one domain value. Horizontal Line Test: If every horizontal line intersects the graph of a function f in no more than one place, then f is a one-to-one function. Example 1: Which of the following functions are one-to-one? Definition: If f is a one-to-one function, then the of f is the function formed by interchanging the independent and dependent variables for f . Thus, if ( a , b ) is a point on the graph of f , then ( b , a ) is a point on the graph of the inverse of f . Example 2: Find the inverse of y = 6 x + 5. 17

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c circlecopyrt Kendra Kilmer January 20, 2009 Definition: The inverse of an exponential function ( y = b x ) is called a logarithmic function . For b > 0 and b negationslash = 1, y = log b x b y = x Example 3: Solve for x , y , or b without a calculator. a) log 3 x = 2 b) log b e 4 = 4 c) log 49 ( 1 7 ) = y Properties of Logarithmic Functions If b , M , and N are positive real numbers, b negationslash = 1, and x is a real number. 1. log b 1 = 0 2. log b b = 1 3. log b b x = x 4. b log b x = x , x > 0 5. log b MN = log b M + log b N 6. log b M N = log b M log b N 7. log b M N = N · log b M 8. log b M = log b N if and only if

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14209an2.17-20 - c Kendra Kilmer Section 2.5 Logarithmic...

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