# Exponential and Logarithmic Functions

## Contents

#### Terms

Base  -  a is the base of the exponential expression a x . a is also the base of the logarithmic expression loga x .
Common Logarithmic Function  -  The logarithmic function f (x) = log10x .
Exponent  -  x is the exponent in the exponential expression a x . It means a is multiplied by itself x times.
Exponential Function  -  A function of the form f (x) = a x , where a > 0 , a≠1 , and x is any real number
Half-life  -  The time it takes for a exponentially decaying substance to lose half its mass.
Logarithm  -  An expression of the form loga x . If loga x = b , a b = x .
Logarithmic Function  -  A function of the form y = loga x where x = a y , a > 0 , and a≠1 . This example is a logarithmic function with base a .
Natural Exponential Function  -  The function f (x) = e x .
Natural Logarithmic Function  -  The logarithmic function f (x) = loge x = ln x .

#### Formulae

 Change of Base loga x = , where a , b , and x are all positive real numbers and a, b≠1 .