# Exponential and logarithmic functions

Contents

Learn about logarithms, which are the inverses of exponents. Use logarithms to solve various equations. Then analyze both logarithmic and exponential functions and their graphs.

Learn how we define logarithms and use this definition in order to evaluate various logarithms. For example, evaluate log_2(8) as 3 by realizing that 2^3=8.

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 about special properties of logarithms that help us rewrite logarithmic expressions in different equivalent (much like we use properties of exponents to rewrite exponential expressions!).

Learn how to rewrite any logarithmic expression in a different base. For example, rewrite log_2(3) as ln(3)/ln(2). This is very helpful for evaluating logarithms with a calculator, which only evaluates base-10 and base-e logarithms.

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

Learn how to solve any exponential equation by using logarithms. For example, solve 2^x=3 by calculating log_2(3).

Learn how to solve word problems that require exponential equations.

Learn about the graphs of advanced exponential functions of the form y=a*b^(x+c)+d.

Learn about the graphs of logarithmic functions, and how they relate to graphs of exponential functions.

Enrich your knowledge with some videos about logarithmic scales and how useful they are.