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Math Help - Two problems about indices and exponential equations

  1. #1
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    Two problems about indices and exponential equations

    Could someone please help me solve them? These were on my test, but I didn't manage to do them.


    1) (x^{2}-5x+5)^{(x^{2}-9)}=1


    2) if 2^{x} =15 and 15^{y}=32
    How much is xy?







    Thank you!
    Last edited by Coach; September 24th 2007 at 06:52 AM.
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Coach View Post
    2) if 2^{x} =15 and 15^{y}=32
    How much is xy?
    x = log_{2} 15

    y = log_{15} 32

    x = \frac{1}{ log_{15} 2 }

    xy = \frac{ log_{15} 32 }{ log_{15} 2 }

    xy = 5
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    Thank you!




    By the way, could one use the zero product property for the first exponential equation?
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by Coach View Post
    Thank you!




    By the way, could one use the zero product property for the first exponential equation?
    I'm not quite sure what you mean by that, give me an example of how it is used?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by janvdl View Post
    I'm not quite sure what you mean by that, give me an example of how it is used?
    i believe he is talking about setting the power equal to zero (since anything raised to zero is 1). i think that's the way to go
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  6. #6
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Coach View Post

    1) (x^{2}-5x+5)^{(x^{2}-9)}=1
    So x = +3 or x = -3 ?

    But that = 1 wasn't there earlier...
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by janvdl View Post
    So x = +3 or x = -3 ?
    yes

    But that = 1 wasn't there earlier...
    yes, that happens from time to time. the instructions were to "solve" so there should have been = something, so if it wasn't there, we would know that something was off with the question
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  8. #8
    Bar0n janvdl's Avatar
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    I tried expanding this:

    (x^{2}-5x+5)^{(x^{2}-9)}

    Because I thought it needed to be expanded...

    By the way, is it anyhow possible to expand something like this?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by janvdl View Post
    I tried expanding this:

    (x^{2}-5x+5)^{(x^{2}-9)}

    Because I thought it needed to be expanded...

    By the way, is it anyhow possible to expand something like this?
    i very much doubt it. i would say no, but i've been seeing some things done in math lately that i would have said was impossible, so it's a "likely" no


    curious: how did you try expanding it?
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by Jhevon View Post
    i very much doubt it. i would say no, but i've been seeing some things done in math lately that i would have said was impossible, so it's a "likely" no


    curious: how did you try expanding it?
    I tried setting values into x and expanding it, and trying to note patterns. Like with series and sequences, if you understand my method.

    Maybe CaptainBlack or TPH can do it...
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  11. #11
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    Yes, I forgot the one at first, I'm sorry.



    Yes I also thought about the zero product property,as 1^{0}=1






    But I guess one could raise each term separately into the power.
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  12. #12
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Coach View Post
    But I guess one could raise each term separately into the power.
    You mean (a + b)^{a + b} = a^{a + b} + b^{a + b} ?

    That's wrong.

    EDIT: Remember (a + b)^{2} = a^{2} + 2ab + b^{2} ?
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  13. #13
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Coach View Post
    Well, I was just guessing.

    But good to know that. Thank you!
    Dont worry, i tried doing that, before realising it was wrong
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    Is there any way one could multiply or raise to a power both sides to eliminate the power?
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  15. #15
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    If anyone knows how to do this, could they please help me?
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