Paul's Online Math Notes
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Cheat Sheets & Tables
Algebra, Trigonometry and Calculus cheat sheets and a variety of tables.
Class Notes
Each class has notes available. Most of the classes have practice problems with solutions available on the practice problems pages. Also most classes have assignment problems for instructors to assign for homework (answers/solutions to the assignment problems are not given or available on the site).
Algebra
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Notes
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Practice Problems
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Assignment Problems
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Calculus I
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Notes
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Practice Problems
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Assignment Problems
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Calculus II
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Practice Problems
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Assignment Problems
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Calculus III
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Notes
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Practice Problems
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Assignment Problems
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Differential Equations
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Notes
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Extras
Here are some extras topics that I have on the site that do not really rise to the level of full class notes.
Algebra/Trig Review
Common Math Errors
Complex Number Primer
How To Study Math
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Current Location : Algebra (Assignment Problems) / Exponential and Logarithm Functions / Solving Exponential Equations
Algebra
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Notes
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Practice Problems
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Assignment Problems
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Preliminaries
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Practice Problems
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Assignment Problems
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Integer Exponents
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Notes
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Practice Problems
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Assignment Problems
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Rational Exponents
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Practice Problems
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Assignment Problems
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Radicals
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Notes
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Practice Problems
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Assignment Problems
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Polynomials
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Notes
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Practice Problems
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Assignment Problems
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Factoring Polynomials
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Notes
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Practice Problems
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Assignment Problems
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Rational Expressions
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Practice Problems
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Assignment Problems
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Complex Numbers
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Notes
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Practice Problems
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Assignment Problems
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Solving Equations and Inequalities
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Notes
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Practice Problems
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Assignment Problems
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Solutions and Solution Sets
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Notes
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Practice Problems
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Assignment Problems
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Linear Equations
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Notes
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Practice Problems
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Assignment Problems
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Applications of Linear Equations
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Practice Problems
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Assignment Problems
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Equations With More Than One Variable
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Practice Problems
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Assignment Problems
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Quadratic Equations - Part I
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Practice Problems
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Assignment Problems
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Quadratic Equations - Part II
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Practice Problems
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Assignment Problems
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Quadratic Equations : A Summary
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Practice Problems
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Assignment Problems
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Applications of Quadratic Equations
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Practice Problems
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Assignment Problems
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Equations Reducible to Quadratic in Form
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Practice Problems
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Assignment Problems
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Equations with Radicals
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Practice Problems
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Assignment Problems
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Linear Inequalities
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Practice Problems
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Polynomial Inequalities
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Practice Problems
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Assignment Problems
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Rational Inequalities
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Practice Problems
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Assignment Problems
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Absolute Value Equations
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Practice Problems
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Absolute Value Inequalities
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Practice Problems
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Assignment Problems
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Graphing and Functions
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Practice Problems
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Assignment Problems
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Graphing
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Assignment Problems
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Lines
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Practice Problems
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Assignment Problems
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Circles
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Practice Problems
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Assignment Problems
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The Definition of a Function
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Practice Problems
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Assignment Problems
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Graphing Functions
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Practice Problems
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Assignment Problems
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Combining Functions
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Practice Problems
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Assignment Problems
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Inverse Functions
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Practice Problems
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Assignment Problems
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Common Graphs
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Practice Problems
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Assignment Problems
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Lines, Circles and Piecewise Functions
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Practice Problems
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Assignment Problems
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Parabolas
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Practice Problems
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Assignment Problems
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Ellipses
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Practice Problems
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Assignment Problems
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Hyperbolas
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Practice Problems
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Assignment Problems
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Miscellaneous Functions
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Practice Problems
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Assignment Problems
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Transformations
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Notes
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Practice Problems
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Assignment Problems
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Symmetry
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Practice Problems
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Assignment Problems
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Rational Functions
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Practice Problems
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Assignment Problems
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Polynomial Functions
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Practice Problems
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Assignment Problems
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Dividing Polynomials
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Practice Problems
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Assignment Problems
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Zeroes/Roots of Polynomials
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Practice Problems
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Assignment Problems
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Graphing Polynomials
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Notes
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Practice Problems
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Assignment Problems
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Finding Zeroes of Polynomials
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Practice Problems
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Assignment Problems
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Partial Fractions
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Practice Problems
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Assignment Problems
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Exponential and Logarithm Functions
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Practice Problems
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Assignment Problems
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Exponential Functions
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Notes
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Practice Problems
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Assignment Problems
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Logarithm Functions
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Practice Problems
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Assignment Problems
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Solving Exponential Equations
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Practice Problems
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Assignment Problems
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Solving Logarithm Equations
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Practice Problems
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Assignment Problems
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Applications
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Practice Problems
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Assignment Problems
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Systems of Equations
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Practice Problems
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Assignment Problems
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Linear Systems with Two Variables
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Practice Problems
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Assignment Problems
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Linear Systems with Three Variables
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Assignment Problems
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Augmented Matrices
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More on the Augmented Matrix
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Practice Problems
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Nonlinear Systems
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Assignment Problems
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If you know exactly which file you'd like to download or you want a file different from any listed below you can go directly to the
Download Page
to get it.
Algebra
- Complete book download links
Notes
File Size : 2.13 MB Last Updated : Wednesday December 20, 2017
Practice Problems
File Size : 286 KB Last Updated : Monday May 30, 2016
Practice Problems Solutions
File Size : 1.86 MB Last Updated : Saturday December 30, 2017
Assignment Problems
File Size : 370 KB Last Updated : Monday June 27, 2016
Exponential and Logarithm Functions
- Complete chapter download links
Notes
File Size : 310 KB Last Updated : Thursday December 1, 2016
Practice Problems
File Size : 136 KB Last Updated : Tuesday February 9, 2016
Practice Problems Solutions
File Size : 375 KB Last Updated : Tuesday February 9, 2016
Assignment Problems
File Size : 133 KB Last Updated : Monday June 27, 2016
Solving Exponential Equations
- Complete section download links
Notes
File Size : 90 KB Last Updated : Saturday July 28, 2007
Practice Problems
File Size : 56 KB Last Updated : Wednesday April 17, 2013
Practice Problems Solutions
File Size : 92 KB Last Updated : Wednesday April 17, 2013
Assignment Problems
File Size : 52 KB Last Updated : Wednesday April 17, 2013
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Contact Me
- Send me an email!
Request Permission for Using Notes
- If you are an instructor and wish to use some of the material on this site in your classes please fill out this form.
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FAQ
- A few frequently asked questions.
Links
- Links to various sites that I've run across over the years.
My Students
- This is for students who are actually taking a class from me at Lamar University.
Privacy Statement
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Site Help
- A set of answers to commonly asked questions. Note that these are identical to those in the "Site Help" menu.
Site Map
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The equations overlap the text! What can I do to fix this?
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If the equations are overlapping the text (they are probably all shifted downwards from where they should be) then you are probably using Internet Explorer 10 or Internet Explorer 11. To fix this problem you will need to put your browser in "Compatibly Mode" (see instructions below). Alternatively, you can view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part.
Put Internet Explorer 10 in Compatibility Mode
Look to the right side of the address bar at the top of the Internet Explorer window. You should see an icon that looks like a piece of paper torn in half. Click on this and you have put the browser in Compatibility View for my site and the equations should display properly.
Put Internet Explorer 11 in Compatibility Mode
Look to the right side edge of the Internet Explorer window. You should see a gear icon (it should be right below the "x" icon for closing Internet Explorer). Click on this to open the Tools menu. Down towards the bottom of the Tools menu you should see the option "Compatibility View Settings". Select this option to open a dialog box. In the "Add this website" box Internet Explorer should already have filled in "lamar.edu" for you, if not fill that in. Then all you need to do is click the "Add" button and you will have put the browser in Compatibility View for my site and the equations should display properly.
Can you help me with a problem/homework/
etc
?
Show Answer
Short Answer :
No.
Long Answer :
No.
Long Answer with Explanation :
I'm not trying to be a jerk with the previous two answers but the answer really is "No". Here's why.
My first priority is always to help the students who have paid to be in one of my classes here at Lamar University (that is my job after all!). I also have quite a few duties in my department that keep me quite busy at times. All this means that I just don't have a lot of time to be helping random folks who contact me via this website. I would love to be able to help everyone but the reality is that I just don't have the time. So, because I can't help everyone who contacts me for help I don't answer any of the emails asking for help.
Also, when I first started this site I did try to help as many as I could and quickly found that for a small group of people I was becoming a free tutor and was constantly being barraged with questions and requests for help. Unfortunately there were a small number of those as well that were VERY demanding of my time and generally did not understand that I was not going to be available 24 hours/day, 7 days/week for help. I really got tired of dealing with those kinds of people and that was one of the reasons (along with simply getting busier here at Lamar) that made me decide to quit answering any email asking for help.
So, while I'd like to answer all emails for help, I can't and so I'm sorry to say that all emails requesting help will be ignored.
Where are the answers/solutions to the Assignment Problems?
Show Answer
Answer/solutions to the assignment problems do not exist. Those are intended for use by instructors to assign for homework problems if they want to. Having solutions (and for many instructors even just having the answers) readily available would defeat the purpose of the problems. Please do not email asking for the solutions/answers as you won't get them from me.
How do I download pdf versions of the pages?
Show Answer
There are a variety of ways to download pdf versions of the material on the site.
From Content Page
If you are on a particular content page hover/click on the "Downloads" menu item. You will be presented with a variety of links for pdf files associated with the page you are on. Included in the links will be links for the full Chapter and E-Book of the page you are on (if applicable) as well as links for the Notes, Practice Problems, Solutions to the Practice Problems and Assignment Problems. The links for the page you are on will be
highlighted
so you can easily find them.
From Download Page
All pdfs available for download can be found on the
Download Page
. Links to the download page can be found in the Download Menu, the Misc Links Menu and at the bottom of each page. Once on the Download Page simply select the topic you wish to download pdfs from. This will present you with another menu in which you can select the specific page you wish to download pdfs for. Once you have made a selection from this second menu up to four links (depending on whether or not practice and assignment problems are available for that page) will show up below the second menu that you can click on to initiate the download.
From Site Map Page
The
Site Map Page
for the site will contain a link for every pdf that is available for downloading. You can access the Site Map Page from the Misc Links Menu or from the link at the bottom of every page.
Note for Internet Explorer Users
If you are using Internet Explorer in all likelihood after clicking on a link to initiate a download a gold bar will appear at the bottom of your browser window that will allow you to open the pdf file or save it.
I've found a typo in the material.
Show Answer
If you have found a typo or mistake on a page them please
contact
me and let me know of the typo/mistake. Please be as specific as possible in your report. Let me know what page you are on and just what you feel the typo/mistake is. It's kind of hard to find the potential typo if all you write is "The 2 in problem 1 should be a 3" (and yes I've gotten handful of typo reports like that...).
Some of the equations are too small for me to see!
Show Answer
This is a problem with some of the equations on the site unfortunately. It is especially true for some exponents and occasionally a "double prime" 2nd derivative notation will look like a "single prime". You can click on any equation to get a larger view of the equation. Clicking on the larger equation will make it go away.
If you are a mobile device (especially a phone) then the equations will appear very small. I am attempting to find a way around this but it is a function of the program that I use to convert the source documents to web pages and so I'm somewhat limited in what I can do. I am hoping they update the program in the future to address this. In the mean time you can sometimes get the pages to show larger versions of the equations if you flip your phone into landscape mode.
Another option for many of the "small" equation issues (mobile or otherwise) is to
download
the pdf versions of the pages. These often do not suffer from the same problems.
Is there any way to get a printable version of the solution to a particular Practice Problem?
Show Answer
Yes. If you want a printable version of a single problem solution all you need to do is click on the "[Solution]" link next to the problem to get the solution to show up in the solution pane and then from the "Solution Pane Options" select "Printable Version" and a printable version of that solution will appear in a new tab of your browser.
Algebra (Assignment Problems) / Exponential and Logarithm Functions / Solving Exponential Equations
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Notes
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Practice Problems
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[
Assignment Problems
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Algebra - Assignment Problems
Polynomial Functions
Previous Chapter
Next Chapter
Systems of Equations
Logarithm Functions
Previous Section
Next Section
Solving Logarithm Equations
Solving Exponential Equations
Solve each of the following equations.
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Logarithm Functions
Previous Section
Next Section
Solving Logarithm Equations
Polynomial Functions
Previous Chapter
Next Chapter
Systems of Equations
Algebra (Assignment Problems) / Exponential and Logarithm Functions / Solving Exponential Equations
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