Introduction to Logarithms

Introduction to Logarithms

Definition

Exponential functions such asare one-to-one and must come with an inverse.  

A logarithmic function is defined as the inverse of this function:  if 

• the logarithm is read as "y equals log base a of x," x is known as the argument of the function.

The two functions of 10 raised to the power of x and its inverse log base 10 of x can be illustrated the graph below: 

• Notice that, since they are inverses of each other, they are reflected across the dotted line of y=x.

2 special types of logarithms

The common logarithm has a base of 10 and can be written as such: 

The natural logarithm has a base of e (approx. 2.71) and can be written as such: 

Sample Problems: Simplifying

1.

                                                    

2.
                                                   

3.

IMPORTANT: The domain of a logarithm  is

Works Cited

Stapel, Elizabeth. "The Common and Natural Logarithms." Purplemath. Available from
    http://www.purplemath.com/modules/logs3.htm. Accessed 02 February 2015[Date] [Month] 2014
 

"Audacity Forum." • View Topic. N.p., n.d. Web. 02 Feb. 2015.