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Math Help - Failure of power and logarithm identities

  1. #1
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    Failure of power and logarithm identities

    Exponentiation - Wikipedia, the free encyclopedia

    I was reading a bit on Wikipedia about the complex exponential function when I found the above link. I'm a bit confused about it, especially the fact that (e^a)^b \neq e^{ab} when a or b are complex numbers. A lot of definitions and proofs seem to use those identities, so I'm curious to know how you're supposed to use them when the identity is not always true.
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  2. #2
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    They are true as long as you are dealing with real numbers!
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  3. #3
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    Well I'm mostly concerned about using the identities for complex numbers. For example, the complex definition of z^a is z^a \equiv e^{a\log z}. How can that be true when \log z^a \neq a\log z when a and z are complex numbers?
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