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Section 5.3 class notes_0

# Section 5.3 class notes_0 - Section 5.3 Logarithmic...

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1 f - Section 5.3 Logarithmic Functions Objective 1: Understanding the Definition of a Logarithmic Function Every exponential function of the form ( ) x f x b = where 0 b and 1 b is one-to-one and thus has an inverse function. The graph of ( ) , 1 x f x b b = and its inverse. To find the equation of 1 f - : Step 1. Change ( ) f x to y : x y b = Step 2. Interchange x and y : y x b = Step 3. Solve for y : ?? Before we can solve for y we must introduce the following definition: Definition of the Logarithmic Function For 0, 0and 1 x b b , the logarithmic function with base b is defined by log b y x = if and only if y x b = . Step 3. Solve for y : y x b = can be written as log b y x = Step 4. Change y to 1 ( ) f x - : 1 ( ) log b f x x - = 5.3.1 Write the exponential equation as an equation involving a logarithm. 5.3.9 Write the logarithmic equation as an exponential equation. ( ) x f x b = (0,1) (1, ) b 1 ( 1, ) b - (1, 0) 1 ( , 1) b - ( ,1) b

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Objective 2: Evaluating Logarithmic Expressions
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Section 5.3 class notes_0 - Section 5.3 Logarithmic...

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