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Chapter 8 Exponential and Logarithmic Functions
by Troy Cole
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Chapter 8 Exponential and Logarithmic Functions

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Chapter 8.1

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Chapter 8.2

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Chapter 8.3

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Chapter 8.4

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Chapter 8.5

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Chapter 8.6

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Exploring Exponential Models

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Exponential function: is a funtion with the general form of y = ab^x

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Growth factor: when b>1

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Decay factor: when b <1

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Asymtote: is a line that a graph approches as "x" or "y" increases in absolute value.

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Properties of Exponential Functions

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A = Pert A: amount in account P: Principle r: annual rate of intrest t: time in years

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Logarithmis Functons as Inverses

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Logarith: the base of a positive number.

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Common logarith: is a logarithm that uses the base ten.

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Logarithmis function: is a inverse of a exponential function.

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Ex. log y = x b

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Properties of Logarithms

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Product Property: log(b) MN = log(b)M + log(b)N

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Quotient Property: log(b) M/N = log(b)M - log(b)N

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Power Property: log(b) M^x = x log(b)M

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Exponential and Logarithmis Equations

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Exponential equation: an equation in the form, b^cx = a.

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Change of base formula: to evaluate a logarithm with any base.

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Logarithmis equation: a equation that contains a logarithmic expression.

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Ex. 7^3x = 20

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7^3x = 20 log7^3x = 20 3xlog7 = log20 x= log20/ 3log7 x=0.5132

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Chapter 8.5

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Natural Logarithms

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Natural logarithm function: the functions inverse.

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Ex. Write 3 ln 6 - ln 8 as a single natural logarithm

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3 ln 6 - ln 8 = ln 6^3 - ln 8 Power Property = ln 6^3/8 Quotient Property = ln 27 Simplify

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