Exponential & logarithmic functions

This topic covers: - Radicals & rational exponents - Graphs & end behavior of exponential functions - Manipulating exponential expressions using exponent properties - Exponential growth & decay - Modeling with exponential functions - Solving exponential equations - Logarithm properties - Solving logarithmic equations - Graphing logarithmic functions - Logarithmic scale
44 exercises available

Radicals (also known as roots) are a generalization of square roots. They are the inverse operation of any power. For example, the 5th root of 32 is 2, because 2⁵=32.

We know how to evaluate square roots of perfect squares. For example, √16=4. What about the other square roots? It's harder to give an exact number, but we can simplify them so we have a better understanding of their value. For example, √32=4⋅√2. Learn more about it in this tutorial.

Just like we can simplify square roots, we can simplify other radicals. This tutorial covers the simplification of higher-index roots. For example, ∜48=2⋅∜3.

Learn how an exponential function behaves as the value of its input increases to positive infinity or decreases to negative infinity. Learn how to graph basic exponential functions.

Learn how to analyze the formulas of basic exponential functions in order to find their common ratio, initial value, and other parameters.

Learn how to construct exponential functions to model real-world situations.

Learn how to construct exponential functions and then analyze them to model and solve real-world problems.

Learn how distinguish between linear and exponential growth, and learn the differences between the end behavior of polynomial and exponential functions.

Learn about different ways of describing the rate of change of exponential functions.

Learn how to analyze real-world quantitative relationships given as tables of values to determine whether they represent linear growth or exponential growth.

Learn about a very special constant in math that has a pivotal role in the world of exponential and logarithmic function, the constant e.

Learn how to solve equations that contain logarithmic expressions. For example, solve log(x)+log(3)=log(7).