Editing Exponentiation (section)

===Powers via logarithms===
The definition of {{math|''e''<sup>''x''</sup>}} as the exponential function allows defining {{math|''b''<sup>''x''</sup>}} for every positive real numbers {{mvar|b}}, in terms of exponential and [[logarithm]] function. Specifically, the fact that the [[natural logarithm]] {{math|ln(''x'')}} is the [[inverse function|inverse]] of the exponential function {{math|''e''<sup>''x''</sup>}} means that one has
: <math>b = \exp(\ln b)=e^{\ln b}</math>
for every {{math|''b'' > 0}}. For preserving the identity <math>(e^x)^y=e^{xy},</math> one must have
: <math>b^x=\left(e^{\ln b} \right)^x = e^{x \ln b}</math>

So, <math>e^{x \ln b}</math> can be used as an alternative definition of {{math|''b''<sup>''x''</sup>}} for any positive real {{mvar|b}}. This agrees with the definition given above using rational exponents and continuity, with the advantage to extend straightforwardly to any complex exponent.