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Math Help - Assignment Logarithmic issue (solved past logs but can't solve last bit)

  1. #1
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    Assignment Logarithmic issue (solved past logs but can't solve last bit)

    Hello MHF! First time poster here, the following is my problem:

    2 log(x) + log(x-1) = 1

    I solved the above by grouping the logs together, resulting in the below:

    log[x^2(x-1)] = 1

    log[x^3-x^2] = 1

    By removing logs I ended up with:

    x^3 - x^2 = 10

    I simply have no idea how to solve this (it's probably simpler than I might imagine) but the x cubed is confusing me and I cannot find anything I can pull out in common that lets me solve with with an answer of 10 for both brackets or whatever.

    Any help is appreciated on the matter.
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    Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)

    Since this equation doesn't have any rational solutions there are a number of different ways of finding the solution for x. Here are some suggestions:
    Interval Bisection
    Cubic Formula (not so common but takes a form similar to the Quadratic Formula)
    Newton-Raphson method

    In any case this equation cannot be solved analytically but we can see that a solution exists between 2 < x < 3. Hope this has given you some ideas
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    Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)

    Quote Originally Posted by OllieC View Post
    Since this equation doesn't have any rational solutions there are a number of different ways of finding the solution for x. Here are some suggestions:
    Interval Bisection
    Cubic Formula (not so common but takes a form similar to the Quadratic Formula)
    Newton-Raphson method

    In any case this equation cannot be solved analytically but we can see that a solution exists between 2 < x < 3. Hope this has given you some ideas
    Thanks for the reply.

    I do recall something along the lines of a solution involving a range, but I can't really figure out the proper method to do so, could you please explain in a little more detail?

    Edit: Does it by any chance involve testing several numbers replacing x and figure out which ones provides a result closest to 0?
    Last edited by Luponius; December 11th 2012 at 02:13 PM.
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    Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)

    The Bisection Method is the easiest to apply. Decide a region which your solution lies in, halve it, then see which half the solution lies in and repeat the process until you have your desired accuracy.
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    Re: Assignment Logarithmic issue (solved past logs but can't solve last bit)

    Thanks kindly!

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