Chapter 6 : Exponential and Logarithm Functions
Here are a set of practice problems for the Exponential and Logarithm Functions chapter of the Algebra notes.
- If you’d like a pdf document containing the solutions the download tab above contains links to pdf’s containing the solutions for the full book, chapter and section. At this time, I do not offer pdf’s for solutions to individual problems.
- If you’d like to view the solutions on the web go to the problem set web page, click the solution link for any problem and it will take you to the solution to that problem.
Note that some sections will have more problems than others and some will have more or less of a variety of problems. Most sections should have a range of difficulty levels in the problems although this will vary from section to section.
Here is a list of all the sections for which practice problems have been written as well as a brief description of the material covered in the notes for that particular section.
Exponential Functions – In this section we will introduce exponential functions. We will give some of the basic properties and graphs of exponential functions. We will also discuss what many people consider to be the exponential function, \(f(x) = {\bf e}^{x}\).
Logarithm Functions – In this section we will introduce logarithm functions. We give the basic properties and graphs of logarithm functions. In addition, we discuss how to evaluate some basic logarithms including the use of the change of base formula. We will also discuss the common logarithm, \(\log(x)\), and the natural logarithm, \(\ln(x)\).
Solving Exponential Equations – In this section we will discuss a couple of methods for solving equations that contain exponentials.
Solving Logarithm Equations – In this section we will discuss a couple of methods for solving equations that contain logarithms. Also, as we’ll see, with one of the methods we will need to be careful of the results of the method as it is always possible that the method gives values that are, in fact, not solutions to the equation.
Applications – In this section we will look at a couple of applications of exponential functions and an application of logarithms. We look at compound interest, exponential growth and decay and earthquake intensity.