Exponentials & logarithms

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This course is a part of Algebra II, a 23-course Topic series from Khan Academy.

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.

This course contains 9 segments:

Introduction to logarithms

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.

The constant e and the natural logarithm

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

Properties of logarithms

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!).

The change of base formula for logarithms

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.

Solving exponential equations with logarithms

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

Solving exponential models

Learn how to solve word problems that require exponential equations.

Graphs of exponential functions

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

Graphs of logarithmic functions

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

Logarithmic scale (optional)

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