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Math Help - Find solutions to logs

  1. #1
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    Find solutions to logs

    I have two problems, which I'd like to put into its own thread. WolframAlpha gives me weird solutions to both of these problems.

    1)

    I'm at a complete loss as in doing this problem .

    2)

    AFAIK, I can use a algebraic property of log to combine parts of the equation:

    If that was correct, then I don't know what to do from there. If it isn't correct, then I still don't know what to do from there.
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  2. #2
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    Quote Originally Posted by BeSweeet View Post
    I have two problems, which I'd like to put into its own thread. WolframAlpha gives me weird solutions to both of these problems.

    1)

    I'm at a complete loss as in doing this problem .

    2)

    AFAIK, I can use a algebraic property of log to combine parts of the equation:

    If that was correct, then I don't know what to do from there. If it isn't correct, then I still don't know what to do from there.
    The algebraic property of logarithms that you referred to is:

    log(a) + log(b) = log(ab) \Rightarrow log(x) + log(x-8) = log(x(x-8)) = log(x^2-8x)

    As for the first:

    Let t=2^x. Remember that 2^{-x} = \frac{1}{2^x} \Rightarrow \frac{1}{t} = 2^{-x}

    So we have: t + \frac{12}{t} - 7 = 0 \Rightarrow t^2 + -7t +12 = 0 \Rightarrow t_{1,2} = \frac{7 \pm \sqrt{49-4\cdot (12)}}{2} = \frac{7 \pm 1}{2} = 4,3

    So we got t=4,3 \Rightarrow 2^x = 4,3 \Rightarrow x = log_{2}(4), log_{2}(3)

    Substitute both these values into the original equation and see if they fit.
    Last edited by Defunkt; October 25th 2009 at 03:51 PM.
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  3. #3
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    Quote Originally Posted by Defunkt View Post
    The algebraic property of logarithms that you referred to is:

    log(a) + log(b) = log(ab) \Rightarrow log(x) + log(x-8) = log(x(x-8)) = log(x^2-8x)
    ...

    Either way, I don't know what to do...
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  4. #4
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    Quote Originally Posted by BeSweeet View Post
    ...

    Either way, I don't know what to do...
    e^{log(x^2-8x)} = e^2

    Can you solve now, using the definition of log?
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  5. #5
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    Quote Originally Posted by Defunkt View Post
    e^{log(x^2-8x)} = e^2

    Can you solve now, using the definition of log?
    I can't .
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