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Exponential and Logarithmic Functions

A series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.

Exponential Functions and their Graphs
There are certain functions, such as exponential functions, that have many applications to the real world and have useful inverse functions. Graphing exponential functions is used frequently, we often hear of situations that have exponential growth or exponential decay. The inverses of exponential functions are logarithmic functions. The graphs of exponential functions are used to analyze and interpret data.

Solving Exponential Equations with the 'Same' Base
In the real world we often hear terms like exponential growth or exponential decay, when discussing solving exponential equations such as those used in compounding interest problems. In order to understand solving exponential equations, students should understand the significance of exponential functions and logarithmic functions.

Introduction to Logarithms
The importance of having inverse functions leads us to the introduction to logarithms as the inverses of exponential functions. Solving exponential equations often involves using the ideas presented in the introduction to logarithms to simplify or access the variable for manipulation. To take the log of an exponential function helps us to use the exponentiated term.

Solving Simple Logarithmic Equations
In order to understand solving logarithmic equations, students must understand the basics of logarithms, and how to use exponentiation to access the terms inside the logarithm. Some more complicated instances of solving simple logarithmic equations require knowledge of the product, quotient and power rules of logarithms in order to simplify complex terms.

Function Notation with Logs and Exponentials
Function notation is used frequently in science to express functions that contain logs and exponents. We learn to use function notation with logs and exponentials in order to solve problems such as computing compounding interest. We can solve these problems written in function notation with logs and exponentials using techniques from solving exponential and log equations.

Graph of Logarithmic Functions
In science classes we will often find ourselves graphing logarithmic functions to describe situations such as motion or speed over time. When trying to identify these situations as those seen in graphing logarithmic functions, it is important to be able to recognize these graphs. It is also important to recognize graphs of exponential functions and their importance as the logarithmic inverse.

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