239
L22 Exponential Functions
Statement
: If
a
and
x
are real numbers with
0
a
>
and
1
a
≠
, then
x
y
a
=
is a uniquely defined real number.
Laws of Exponents
If
s
,
t
,
a
, and
b
are real numbers, with
0
a
>
,
0
b
>
,
then
s
t
s
t
a
a
a
+
⋅
=
s
s
t
t
a
a
a
−
=
(
)
s
t
st
a
a
=
0
1
a
=
(
)
s
s
s
ab
a
b
=
⋅
s
s
s
a
a
b
b
⎛
⎞
=
⎜
⎟
⎝
⎠
1
1
s
s
s
a
a
a
−
⎛
⎞
=
=
⎜
⎟
⎝
⎠
The
exponential function
with the base
a
is a
function of the form
( )
x
f x
a
=
,
where
0
a
>
and
1
a
≠
.
The domain of
f
is the set of all real numbers.

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