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Math Help - exponents and powers

  1. #1
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    exponents and powers

    i got this question in my exam today

    find x if 163x=325x-13

    i keep getting it as 65/17 which i know is wrong.i really want to find my mistake before the papers are out.
    a friend of mine got the answer as 8 but he's not sure either.please help.

    thanks in advance
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: exponents and powers

    You are both incorrect. We are given:

    16^{3x}=32^{5x-13}

    Since both bases are powers of 2, we may write:

    (2^4)^{3x}=(2^5)^{5x-13}

    2^{12x}=2^{25x-65}

    Now, equate the exponents, and solve for x.
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  3. #3
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    Re: exponents and powers

    yes i did get that part.
    then since the base is common,
    12x=25x-65
    65=25x-12x
    65=17x
    x=65/17

    hmmmm is there anything wrong with this? cuz actually i wasn't present when this topic was being taught.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: exponents and powers

    25-12=13
    Thanks from NormalKid
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  5. #5
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    Re: exponents and powers

    How could I be so stupid?!
    Why does It always happen to me.?!!
    Last edited by NormalKid; October 3rd 2012 at 09:12 PM.
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  6. #6
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    Re: exponents and powers

    yes it is
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  7. #7
    MHF Contributor MarkFL's Avatar
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    Re: exponents and powers

    Yes, that is the correct solution.

    As for not making simple mistakes, I will let you know if I ever stop making them!
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  8. #8
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    Re: exponents and powers

    Ah............no one is perfect.
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