Inverses
Site: | Clare-Gladwin RESD |
Course: | Michigan Algebra I |
Book: | Inverses |
Printed by: | Guest user |
Date: | Wednesday, January 15, 2025, 3:43 PM |
Description
Inverses
Introduction
Just like all families of functions, exponential functions have an inverse. To find the inverse, switch the x and y values of the graph, table or equation to see the new function.
Example Graph the inverse of the function: y = 2x.
Step 1. Make a table of values.
Step 2. Switch the values of x and y in the table.
Step 3. Plot the points on a coordinate plane.
Logarithms
The graph in the previous example can be modeled by the function y = log2 x. Logarithms are the inverse of exponentials, just as subtraction is the inverse of addition, and division is the inverse of multiplication. Translating exponential functions into logarithmic functions always follows the form below:y = bx is equivalent to logb( y) = x
The right-hand side above is pronounced, "log-base-b of y equals x". The value of the subscripted "b" is the base of the logarithm, just as b is the base in the exponential equation. And, just as the base b of an exponential is always positive and never equal to 1, so is the base b for a logarithm.
* Note: Finding the logarithm that corresponds to the exponential function will be covered in Algebra II. Look at the following examples as a way to introduce yourself to the idea that will be covered later.
Examples
Example 1Convert 63 = 216 to the equivalent logarithmic equation.
To convert, the base remains the same, but the 3 and the 216 switch sides.
log 6 (216) = 3
Example 2
Convert log4(1024) = 5 to the equivalent exponential equation.
To convert, the base remains the same, but the 1024 and the 5 switch sides.
4 5 = 1024
Practice
Inverses of Exponentials WorksheetAnswer Key
Inverses of Exponentials Answer KeySources
Khan, Salman. " An introduction to logarithms."
http://www.khanacademy.org/video/introduction-to-logarithms (accessed September 12, 2010).
Stapel, Elizabeth. "Logarithms: Introduction to 'The Relationship'." Purplemath. Available from http://www.purplemath.com/modules/logs.htm. Accessed 12 September 2010