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 03:06 PM.
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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...
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!
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.
Originally Posted by DrSteve 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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