# Glossary for Lesson 31: Logarithmic Functions

### Logarithmic Function

A logarithmic function is a function that can be written in the form

f(x)=\log_ax

Here, a is the base of the logarithmic function, and a is positive number not equal to 1.  The domain of a function of this form is x>0.  The equation y=\log_ax is true if and only if x=a^y

### Logarithm

A logarithm is an expression of the form \log_ab, and it represents the number that a would need to be taken to the power of in order to equal b.  For example, log_39 is equal to 2

### Natural Logarithmic Function

The natural logarithmic function is the logarithmic function with base e, but it is usually written with a different notation:

f(x)=\log_ex=\ln x

The natural log has many real-world applications, especially in growth and decay of natural systems and half-lives of isotopes.