Inverse, Exponential, and Logarithmic Functions Chapter 13 Inverse, Exponential, and Logarithmic Functions

Sect. 13.1 Inverse Functions Only one-to-one functions have inverses. Ex. 1

One-to-One Example continued

Use the horizontal line test to Determine if a Function is One-to-One Ex. 2

Find the Inverse of a One-to-One Function Ex. 3

Finding the Inverse of a One-to-One Function Ex. 4

Finding the Relationship between a Function and Its Inverse Ex. 5

Finding the Relationship between a Function and Its Inverse continued

Given the Graph of f(x), Graph f-1(x) Ex. 6

Given the Equations of f(x) and f-1(x), Show That Ex. 7

Sect. 13.2 Exponential Functions

Graph an Exponential Function

Another Exponential Graph

Graph an Exponential Function of the Form f(x) = ax+c

Define the Irrational Number e and Graph f(x) = ex

Ex. 5 Solve an Exponential Equation by Expressing Both Sides of the Equation with the Same Base

Solve an Exponential Equation by Expressing Both Sides of the Equation with the Same Base continued

Solve an Applied Problem Using a Given Exponential Function

Sect. 13.3 Logarithmic Functions

Rewrite an Equation in Logarithmic Form as an Equation in Exponential Form

Rewrite an Equation in Exponential Form as an Equation in Logarithmic Form

Solve a Logarithmic Equation of the Form logab = c Ex. 3

Solve a Logarithmic Equation of the Form logab = c continued

Ex. 4 Evaluate a Logarithm

Evaluate Common Logarithms, and Solve Equations of the Form log b = c Ex. 5

Solving a Logarithmic Equation Ex. 6

Use the Properties logaa = 1and loga1 = 0 Ex. 7

Define and Graph a Logarithmic Function Ex. 8

Graph a Logarithmic Function Ex. 9

Another Logaritmic Graph Ex. 10

Solve an Applied Problem Using a Given Logarithmic Equation Ex. 11

Solve an Applied Problem Using a Given Logarithmic Equation continued

Sect. 13.4 Properties of Logarithms Ex. 1 Using the Product Rule

Using the Product Rule continued Ex. 2

Use the Quotient Rule for Logarithms Ex. 3

More Examples of Using the Quotient Rule

Use the Power Rule for Logarithms Ex. 5

Use the Power Rule for Logarithms cont.

Use the Properties logaax = x and alogax = x Ex. 6

Combine the Properties of Logarithms to Rewrite Logarithmic Expressions

More Examples of Combining Properties

More Examples of Combining Properties = 0.5(0.7782) = 0.3891

Sect. 13.5 Common and Natural Logarithms and Change of Base

Evaluate Common Logarithms Using a Calculator Ex. 2

Solve an Equation Containing a Common Logarithm Ex. 3 Ex. 4

Solve an Applied Problem Given an Equation Containing a Common Logarithm Ex. 5

Define a Natural Logarithm

Evaluate Natural Logarithms Without a Calculator Ex. 6 Ex. 7

Solve an Equation Containing a Natural Logarithm Ex. 8

Solve Applied Problems Using Exponential Functions Definition: Compound Interest: The amount of money, A, in dollars, in an account after t years is given by where P (the principal ) is the amount of money (in dollars) deposited in the account, r is the annual interest rate, and n is theniumber of times the interest is compounded per year.

Continuous Compounding Ex. 10

Use the Change-of-Base Formula Ex. 11

Sect. 13.6 Solving Exponential and Logarithmic Equations Ex. 1 Solve by taking ln of both sides

Solving an Exponential Equation ln5

Another Example of Solving an Exponential Equation

Solve Logarithmic Equations Using the Properties of Logarithms Ex. 4

Solve Logarithmic Equations Using the Properties of Logarithms continued

Solve an Equation Where One Term Does Not Contain a Logarithm Ex. 5

Solve Applied Problems Involving Exponential Functions Using a Calculator

Doubling Time Ex. 7

Solve an Applied Problem Involving Exponential Growth or Decay

Solve an Applied Problem Involving Exponential Growth or Decay continued