sparknotes
Exponential and Logarithmic Functions
Terms and Formulae
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
.
|
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