View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Logarithm and Exponential Functions PowerPoint presentation | free to download - id: 3b3e21-ZTk4O

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Logarithm and Exponential Functions

- Overview of logs and exponential functions
- Logarithm is an exponent
- Inverse functions
- Log functions and exponential functions are

inverses of one another - Properties of logarithms
- Logarithms/exponentials in scientific and

real-life problems - Derivatives of log and exponential functions

Exponential functions

- Let bgt0. Then bx well defined if x an integer,

rational number. OK if x is irrational by

continuity. (Filling in holes) - Different behavior if bgt1 or 0ltblt1

Properties of exponential functions

- bgt0 then domain of bx is all real numbers x
- Range is (0,?) (if b?1)
- bx is differentiable
- Power laws

Logarithm is an exponent

- Key fact logbx is unique number so that

- Summary logbx and bx are inverses
- Domain logb x Range bx (0, ?)
- Range logb x Domain bx (- ?, ?)

Concrete Examples

- Compute the following logarithms

Key facts about logs

- logbx only defined for xgt0
- Law of logs

Common logarithms

- Usually deal with log10 x log x or loge x ln

x - Number e

Equations involving logs, exp

- Example Solve ln (x1)5
- Example Solve ex-3e-x 2
- Example Rewrite

Logarithms in Science

- Richter scale
- M Magnitude of earthquake in Richters
- E Released energy (joules)
- Richter formula

Earthquake questions

- Find a formula for E (energy released)
- Question If energy of one earthquake is 10 times

greater, then whats difference in Richters? - Concrete Examples 1994 Northridge was 6.8.

Approximately how much stronger - Kobe 7.2?
- 1906 San Francisco 7.8?
- 1964 Alaska 8.4?

Real life exponential problem

- Receive 10000 at age 20 and invest in mutual

fund until retire _at_ age 70. - How much money if fund earns
- 10?
- 15?

Financial Analysis

Derivative of exponential functions

The exponential function, exp (x)

Examples

More Examples

Inverse Functions

- Example f(x)3x1, g(x)(x-1)/3
- f(g(x))3(x-1)/31x
- More generally, say f and g are inverse functions

if - f(g(x))x for all x in domain of g
- g(f(x))x for all x in domain of f
- In this case, write gf -1

Differentiating Inverse Functions

- Find the derivative of y f -1(x)
- Step 1 Apply f to both sides to get x f(y)
- Step 2 Differentiate
- Step 3 Conclude that

Example

- Consider y f(x) x13 2x 5.
- Compute the derivative of its inverse x f

-1(y) using above formula. - Compute the derivative of its inverse using

implicit differentiation.

Inverse tangent, arctan x

Derivative of log functions

Examples

- Compute the derivatives of the following

functions

Logarithmic Differentiation

- General Strategy Differentiate complicated

function y f(x) by simplifying and (implicitly)

differentiating both sides of ln y ln

f(x)

Derivatives of irrational powers of x

- Let y xr , xgt0, where r is a real number
- Differentiate ln y ln xr
- Conclude that for all real numbers have power law

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Logarithm and Exponential Functions" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Jhu University and other schools with their online training by sharing educational presentations for free