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Math Help - Logarithmic Equation

  1. #1
    Junior Member BobBali's Avatar
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    Logarithmic Equation

    Hello,

    Need help with solving the following log equation:

    3Log(2x) = x-3

    I have tried every possible method using log principles, but i am not getting the same answer as that when i use a GDC to look for the intersects. Please help.
    Last edited by BobBali; May 9th 2010 at 10:17 AM.
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  2. #2
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by BobBali View Post
    Hello,

    Need help with solving the following log equation:

    3Log(2x) = x-3

    I have tried very possible method using log principles, but i am not getting the same answer as that when i use a GDC to look for the intersects. Please help.
    Code:
    >> syms x;
    >> solve('3*log(2*x) = x-3',x)
     
    ans =
     
    1/(2*exp(1)*exp(lambertw(0, -1/(6*exp(1)))))
    
    W = LAMBERTW(X) is the solution to w*exp(w) = x.
    W = LAMBERTW(K,X) is the K-th branch of this multi-valued function.
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  3. #3
    Junior Member BobBali's Avatar
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    Urrr..

    I was hoping a detailed step-by-step method was going to be shown. I want to know how we get the answer to 'x' ?
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  4. #4
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by BobBali View Post
    I was hoping a detailed step-by-step method was going to be shown. I want to know how we get the answer to 'x' ?
    sorry you're disappointed, but the fact is that you'll not be able to solve this equation using elementary algebraic techniques.

    the previous response shows a computer generated solution using the Lambert W function.

    my advice to you is to get out your calculator and solve it.

    graph y = 3\log(2x) - (x-3) and look for the real zero.
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  5. #5
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by BobBali View Post
    I was hoping a detailed step-by-step method was going to be shown. I want to know how we get the answer to 'x' ?
    Sorry, I tried to do this at first...

    Had to resort to MATLAB.
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  6. #6
    Junior Member BobBali's Avatar
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    Are you Serious?

    I cant solve this equation by hand..?! Oh, man... Yes, when i punched it originally into my GDC and looked for the intercept i got x = 6.3 , which checks out when i replace x in the equation. But, i was under the impression it could be solved by hand, apart from taking x/y values and plotting on a graph-paper by hand and looking for the intercepts... How did the Math-Gurus do it 30years ago?? They just graphed it by hand?
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