3.2 Logarithmic Functions

Since the graph of an exponential function passes the horizontal line test, it must have an inverse.  The inverse of an exponential function is a logarithmic function.

The logarithmic equation can be read as "y equals the log base a of x".  This means that a to the yth power equals x.

Logarithms have properties:

 

if,  then

The following features of exponential graphs are the corresponding features of logarithmic graphs.

Exponential                                   Logarithmic

Horizontal Asymptote                   Vertical Asymptote

Y-Intercept                                    X-Intercept

Domain                                          Range

Range                                            Domain

ln x is log base "e", also called the natural log.  "e" is simply a number equaling 2.7182....etc. 

Logarithmic functions can be transformed.

-a vertically stretches the graph.

-b is the base.  The bigger the base, the slower the graph grows.  If the base is less than one, the graph     flips over the x- axis.  The base can't be negative.

-c shifts the graph left and right.

-d shifts the graph up and down.

Have fun!!!!