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Math Help - Equation Proofs

  1. #1
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    Equation Proofs

    I am having a lot of difficulty figuring this one out. The goal is to show that equations 1, 2, and 3, give the final simplified equation 4. I have always been more of a calculus person, and have trouble with these types of algebra problems.



    So far I have tried multiplying both S and Sigma together and attempted to put ga into the equation, which didn't really get me anywhere. Any help is appreciated!
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  2. #2
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    I would plug Equations 2 and 3 into 4 and show that you get Equation 1, for an appropriate choice of N. Then, since all your steps are reversible, you've shown that which you were asked to show.
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  3. #3
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    I plugged both 2 and 3 into the last equation and it simplified to this:



    The exponents still look incorrect and I missing something?
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  4. #4
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    Nothing incorrect yet. Remember the laws of exponents, and simplify your expression a bit.
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  5. #5
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    I was able to simplify the exponents a lot, and it looks better:

    I am still stuck with the ga term on the bottom though
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  6. #6
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    You should have

    g_{a}^{n_{b}} on the bottom.

    You now must choose the value of N that makes it all work the same as Equation # 1.
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  7. #7
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    Correct, I just saw that I forgot to raise the bottom ga to the nb power, that makes so much more sense!
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  8. #8
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    So, what's N?
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  9. #9
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    Would it happen to be N= n_b^2, that way the ga term on the bottom would disappear completely leaving only the ga^nb on the top?
    Last edited by 360modina; February 22nd 2011 at 10:44 AM.
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  10. #10
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    Not quite. You need to end up with g_{a}^{n_{a}} on top. Right now, you have g_{a}^{N} on top, and g_{a}^{n_{b}} on the bottom. Use the laws of exponents. What must N be?
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  11. #11
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    N= n_a+n_b
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  12. #12
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    There you go. I'd say you're done now, essentially. Just run your computations in reverse, and you can show that Equations 1-3 give you Equation 4.
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