This lesson considers functions of the form y = a logb x. Known as logarithmic functions, these functions are useful in measuring numeric values that represent natural phenomena such as sound intensity and the strength of earthquakes. In this lesson, you will investigate the characteristics of a logarithmic function by exploring its graph and equation. Before you begin this exploration, you must be familiar with some notation.
The form y = logb x is read y is the log base b of x. Any positive number (other than 1) is a suitable base for a logarithm, but the bases 10 and e are used most often. The a-value is 1.
A logarithm with a base of 10 is called the common logarithm. The common logarithm can be written in two ways.
 |
 |
A logarithm with a base of e is called the natural logarithm. The natural logarithm can also be written in two ways.
 |
 |
Most graphing calculators have distinct keys for inputing logarithms. Use 
for common logarithms and 
for natural logarithms.