# 4: Exponential and Logarithmic Functions

- Page ID
- 34900

In this chapter, we will explore exponential functions, which can be used for, among other things, modeling growth patterns such as those found in bacteria. We will also investigate logarithmic functions, which are closely related to exponential functions. Both types of functions have numerous real-world applications when it comes to modeling and interpreting data.

- 4.1: Exponential Functions
- Define exponential functions. Compare linear and exponential growth. Evaluate exponential functions. Construct a basic exponential equation y = a(b^x) given two given points or a graph. Compound and Continuous Interest. Continuous exponential growth or decay formula y = a e^(rt)

- 4.2: Graphs of Exponential Functions
- Graph equations of the form y=ab^{x+c}+d and y=ab^{-x+c}+d using transformations. Construct an equation from a description or a graph that has been shifted or/and reflected. Manipulate exponential expressions using the exponential properties (product, quotient and power rules) "in reverse".

- 4.3: Logarithmic Functions
- Convert between log and exponential form. Evaluate logarithms by using the definition of the exponential equivalent. Use common and natural logarithms. Evaluate common and natural logs on a calculator.

- 4.4: Graphs of Logarithmic Functions
- Graph log functions using transformations (vertical and horizontal shifts and reflections, vertical stretches). Determine the domain and vertical asymptote of a log function algebraically.

- 4.5: Logarithmic Properties
- Log properties: Properties of One, Inverse Properties, Product, Quotient and Power Rules. Expansion and Condensing of log expressions. Change of Base formula. Applications given formulas involving logarithms.

- 4.6: Exponential and Logarithmic Equations
- Solve exponential equations by using a common base and the one-to-one property or rewriting in log form. Solve exponential equations that are quadratic in form. Solve log equations by using the one-to-one property or by rewriting in exponential form.

- 4.7: Exponential and Logarithmic Models
- Exponential applications: compound and continuous interest, exponential growth, exponential decay, Newton's heating and cooling, logistic growth.

*Thumbnail: The functions \(y=e^x\) and \(y=\ln(x)\) are inverses of each other, so their graphs are symmetric about the line \(y=x\). Image used with permission (CC BY-SA; OpenStax).*

## Contributors

Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus.