A real number raised to a real exponent
is defined by
Prove the following properties:
-
.
-
.
-
.
-
.
- For
,
if and only if
.
- For all of these we use the definition
- Proof.
- Proof.
- Proof.
- Proof.
- Proof. Assume
. For the forward direction, assume
. We have
Therefore, since
we have
, and so
Conversely, if
then we have



