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Math Help - Prove the 4th Law of Exponents

  1. #1
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    Prove the 4th Law of Exponents

    Here is what I did, but I'm not sure that this is valid:

    (ab)^x = e^{x ln(ab)} = e^{x ln(a) + x ln(b)} = e^{x ln(a)}e^{x ln(b)} = a^xb^x

    What do you think?

    Thanks!
    Last edited by mr fantastic; April 18th 2011 at 02:06 PM.
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  2. #2
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    I assume you would not be able to use logarithm laws until you have proven all of the index laws...

    I would say...

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  3. #3
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    That's a good idea. They show us how they prove the first two laws of exponents, and they use logarithms to do it. My attempt is a variation on what the book did for the first two proofs.

    I'll try your way, too.

    Thanks!
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  4. #4
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    Prove It's argument only works if x is a positive integer. A more formal proof (for x a positive integer) would require mathematical induction.

    For x an arbitrary real number, the OP's method can be used.
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  5. #5
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    Quote Originally Posted by DrSteve View Post
    Prove It's argument only works if x is a positive integer. A more formal proof (for x a positive integer) would require mathematical induction.

    For x an arbitrary real number, the OP's method can be used.
    Assuming of course that logarithm rules can be used...
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