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Math Help - Exponential equation

  1. #1
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    Exponential equation

    I've banged my head senseless on an exponential equation lately. I can't seem to solve however i try. Any help would be appreciated.

    problem:

    4^2x - 4^x = 8 * 4^(x+3)

    solve for x

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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by bael View Post
    problem:

    4^2x - 4^x = 8 * 4^(x+3)

    solve for x
    This equation can be written 4^{x}\left(4^x-1\right)=8\times 4^x\times 4^3 and one can divide both sides by 4^x since for all x, 4^x\neq0.

    Can you take it from here ?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by bael View Post
    I've banged my head senseless on an exponential equation lately. I can't seem to solve however i try. Any help would be appreciated.

    problem:

    4^2x - 4^x = 8 * 4^(x+3)

    solve for x

    Lets assume the equation is:

    4^{2x}-4^x=8 \times 4^{x+3}

    or:

    4^{2x}-4^x=8 \times 4^3 \times 4^{x}

    rearrange:

    (4^{x})^2-513\times 4^x=4^x(4^x-513)=0

    so either 4^x=0 which is impossible or:

     <br />
4^x=513<br />

    and you should be able to finish this yourself from that.

    CB
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  4. #4
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    Quote Originally Posted by bael View Post
    I've banged my head senseless on an exponential equation lately. I can't seem to solve however i try. Any help would be appreciated.

    problem:

    4^2x - 4^x = 8 * 4^(x+3)

    solve for x

    4^{2x}-4^x=8*4^{x+3}

    4^x*4^x-4^x=8*4^x*4^3

    4^x(4^x-1)=8*4^x*4^3 and since 4^x\not=0 at anypoint we can divide by it

    4^x-1=8*64

    you good from here?
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  5. #5
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    thanks a lot to all of you. I think I've been everything except this solution, thank you for opening my eyes!!
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