8.4 Logarithmic Functions

1 / 21

# 8.4 Logarithmic Functions - PowerPoint PPT Presentation

8.4 Logarithmic Functions. Standards 11, 14. Goal 1: Evaluate logarithmic functions Goal 2: Graph logarithmic functions. When is it used?. Tornado speeds. Earthquake energy . Goal 1: Evaluate logarithmic functions. Logs. We know that . and. but what is x when. ?.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about '8.4 Logarithmic Functions' - roch

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
8.4 Logarithmic Functions

Standards 11, 14

• Goal 1: Evaluate logarithmic functions
• Goal 2: Graph logarithmic functions
When is it used?

Earthquake energy

Goal 1: Evaluate logarithmic functions

Logs

We know that

and

but what is x when

?

Definition of logarithm with base b

Goal 1: Evaluate logarithmic functions

Examples

Rewrite the exponential form to logarithmic form or vice versa.

Goal 1: Evaluate logarithmic functions

White boards

Rewrite the exponential form to logarithmic form or vice versa.

Goal 1: Evaluate logarithmic functions

Evaluating Log Expressions

3 to what power is 81?

5 to what power is 0.04?

1/2 to what power is 8?

Goal 1: Evaluate logarithmic functions

White Boards

Goal 1: Evaluate logarithmic functions

Common & Natural Logs

Common Log

log with base 10

Natural Log

log with base e

Goal 1: Evaluate logarithmic functions

Notes

Evaluating Log & ln Expressions

Goal 1: Evaluate logarithmic functions

White

Boards

Evaluating Log & ln Expressions

Goal 1: Evaluate logarithmic functions

Review Inverses

Inverses: +/- x/÷ square, square root

Goal 2: Graph Log Functions

Notes

Exponential functions and logarithmic functions undo each other

Goal 2: Graph Log Functions

Notes

Shortcut

Simplify the expression.

Original Problem

make = y

log and base cancel

Rewrite in log form

logs cancel out

Goal 2: Graph Log Functions

Notes

Shortcut

Simplify the expression.

Original Problem

make = y

Rewrite in exponential form

bases cancel out

Goal 2: Graph Log Functions

White

Boards

Notes

Find the inverse of the function.

Original problem

Switch x and y

Rewrite in exponential form; isolate y

The inverse of

is

Goal 2: Graph Log Functions

Notes

Find the inverse of the function.

Original problem

Switch x and y

Rewrite in exponential form; isolate y

;

The inverse of

is

Goal 2: Graph Log Functions

Find the inverse of the function.

Goal 2: Graph Log Functions

Graphing Logs

h: the line x = h is the VERTICAL asymptote

b: if b > 1, then graph moves up and right (⟰,⇛)

if 0<b < 1, then graph moves down and right (⟱,⇛)

(⟱,⇛)

(⟰,⇛)

Goal 2: Graph Log Functions

Graph Logs

Graph the function. State the domain and range.

0 < b < 1

down and right;

almost flattens

asymptote

x = 0

Goal 2: Graph Log Functions

Graph Logs

Graph the function. State the domain and range.

b > 0

up and right;

almost flattens

asymptote

x = -2

Goal 2: Graph Log Functions