Terms
Base

a
is the base of the exponential expression
a
^{x}
.
a
is also the base
of the logarithmic expression
log_{a}
x
.
Common Logarithmic Function

The logarithmic function
f (x) = log_{1}0x
.
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
Halflife

The time it takes for a exponentially decaying substance to lose half its
mass.
Logarithm

An expression of the form
log_{a}
x
. If
log_{a}
x = b
,
a
^{b} = x
.
Logarithmic Function

A function of the form
y = log_{a}
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) = log_{e}
x = ln x
.
Change of Base

log_{a}
x =
, where
a
,
b
, and
x
are all positive
real numbers and
a, b≠1
.
