MA 22000 Lesson 39 Lesson Notes
(2nd half of text) Section 4.4, Logarithmic Functions
Definition of General Logarithmic Function:
A logarithmic function, denoted by
logb
yx
, is equivalent to
y
bx
.
In previous algebra classes, you may have often used the number 10 as a base for a logarithmic
function. These were called common logarithms. In calculus, the most useful base for
logarithms is the number e. These are called natural logarithms.
Definition of the Natural Logarithmic Function:
The natural logarithmic function is denoted by
lnyx
, which is equivalent to saying
loge
yx
. The function
lnyx
is true if and only if
y
ex
. The natural logarithmic function
is the inverse of the natural exponential function.
The Natural Logarithmic function can be written in logarithmic form or exponential form.
Examine the comparison below.
log
logarithmic form: log exponential form:
ln
logarithmix form: ln exponential form:
y
b
y
b
y
y
y x b x
y x x b
y x e x
y x x e
(For the natural logarithmic function: the x is called the argument, the y is called
the logarithm, and the base is the number e .)
Base Argument Logarithm
