Videos and lessons with examples and solutions to help High School students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Common Core: HSF-BF.B.5

Ex: Graph an Exponential Function and Logarithmic Function

This video explains how to graph an exponential and logarithmic function on the same coordinate plane. The two functions are inverses.
Ex: Find the Inverse Function of an Exponential Function

This video explains how to determine the inverse function of an exponential function in the form f(x)=ae^{bx}.

Inverse Properties of Logs

In this video we use the fact that logs and exponentials are inverses in order to simplify expressions.
Inverse Property of Exponentials and Logarithms

This video explains and applies the inverse property of exponentials and logarithms.

Wolfram Inverse Composition Rule

If f(x) is the inverse function of g(x), then f(g(x)) = g(f(x)) = x . In this Demonstration you can choose two functions f and g. The graphs of f and g are drawn with red and blue dashes. Choose the composition f(g(x)) or g(f(x)). The graph of the composition is drawn as a solid green curve. If it is the line y = x , the functions are inverses of each other. If the solid curve is only partly the same as the line y = x , the domain of the functions has to be restricted.

Select the exponent and logarithm functions and you will find that the composition is the green line y = x

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Ex: Graph an Exponential Function and Logarithmic Function

This video explains how to graph an exponential and logarithmic function on the same coordinate plane. The two functions are inverses.

This video explains how to determine the inverse function of an exponential function in the form f(x)=ae

In this video we use the fact that logs and exponentials are inverses in order to simplify expressions.

This video explains and applies the inverse property of exponentials and logarithms.

If f(x) is the inverse function of g(x), then f(g(x)) = g(f(x)) = x . In this Demonstration you can choose two functions f and g. The graphs of f and g are drawn with red and blue dashes. Choose the composition f(g(x)) or g(f(x)). The graph of the composition is drawn as a solid green curve. If it is the line y = x , the functions are inverses of each other. If the solid curve is only partly the same as the line y = x , the domain of the functions has to be restricted.

Select the exponent and logarithm functions and you will find that the composition is the green line y = x

Inverse Composition Rule from the Wolfram Demonstrations Project by Ed Pegg Jr

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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