Exponential and Logarithmic Functions
Lessons in this chapter
About Exponential and Logarithmic Functions
Exponential and Logarithmic Functions builds both function families side by side, showing how one undoes the other.
Exponential Functions and their Graphs and Natural Base Exponential Function cover graphing exponential growth and decay, including the special base e used in continuous growth.
Logarithmic Expressions, Functions, and Graphs introduces logarithms as the inverse operation to exponentiation, along with their own graphs, before Transformations of Exponential and Logarithmic Functions covers shifting and stretching both families.
Properties of Logarithm gives the rules for combining and simplifying logarithms, Exponential and Logarithmic Equations and Inequalities applies them to solve real equations, and Conversion Model of Exponential and Logarithmic Functions closes the chapter by modeling real growth and decay situations.
All seven lessons open as worksheets in the page, from Exponential Functions and their Graphs through Properties of Logarithm to Exponential and Logarithmic Equations and Inequalities. The practice problems are scored as you answer them, which matters most on the logarithm rules, where an error is easy to miss by eye. Free to practice online.
Frequently asked questions
Exponential Functions and their Graphs and Natural Base Exponential Function cover growth, decay, and the constant e. Logarithmic Expressions, Functions, and Graphs introduces the logarithm as the inverse of an exponential, Transformations of Exponential and Logarithmic Functions shifts and stretches both, and Properties of Logarithm gives the product, quotient, and power rules. Exponential and Logarithmic Equations and Inequalities and Conversion Model of Exponential and Logarithmic Functions close with solving and with moving between the two forms. This sits in Functions (F) in the high school Common Core, with the equation solving in Algebra (A).
An exponential function has the input in the exponent, producing repeated multiplicative growth or decay rather than the repeated addition of a linear function.
The natural base e (approximately 2.718) arises naturally in continuous growth situations, like continuously compounded interest.
A logarithm answers the question "what exponent gives this result": log_b(x) = y means b^y = x, making logarithms the inverse operation of exponentiation.
An exponential function's graph and its logarithmic inverse's graph are reflections of each other across the line y = x, since they undo each other.
The product, quotient, and power properties of logarithms let you expand a single complex logarithm into simpler pieces, or combine several logarithms into one.