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Chapter 8 Exponential and Logarithmic Functions by Mind Map: Chapter 8
Exponential and Logarithmic Functions
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Chapter 8 Exponential and Logarithmic Functions

Chapter 8.1

Chapter 8.2

Chapter 8.3

Chapter 8.4

Chapter 8.5

Chapter 8.6

Exploring Exponential Models

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

Growth factor: when b>1

Decay factor: when b <1

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

Properties of Exponential Functions

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

Logarithmis Functons as Inverses

Logarith: the base of a positive number.

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

Logarithmis function: is a inverse of a exponential function.

Ex. log y = x b

Properties of Logarithms

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

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

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

Exponential and Logarithmis Equations

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

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

Logarithmis equation: a equation that contains a logarithmic expression.

Ex. 7^3x = 20

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

Chapter 8.5

Natural Logarithms

Natural logarithm function: the functions inverse.

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

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