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Math Help - Is this very simple equation impossible to solve without graphs or trial and error ?

  1. #1
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    Is this very simple equation impossible to solve without graphs or trial and error ?

    Hi,

    This very simple equation 7^x = 6^x +2 provides an approximate solution of 1.2808
    when using graphs.

    The caret sign "^" represents exponentiation.

    I could easily also represent this problem as 4^x=3^x+7 where x is 2 - but how do you calculate x?

    I cannot find the solution to this problem using logarithms.

    I must be missing something very simple here - could some genius please enlighten me.

    Regards,

    Zorrozac
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  2. #2
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    Quote Originally Posted by zorrozac View Post
    Hi,

    This very simple equation 7^x = 6^x +2 provides an approximate solution of 1.2808
    when using graphs.

    The caret sign "^" represents exponentiation.

    I could easily also represent this problem as 4^x=3^x+7 where x is 2 - but how do you calculate x?

    I cannot find the solution to this problem using logarithms.

    I must be missing something very simple here - could some genius please enlighten me.

    Regards,

    Zorrozac
    Are you only looking for closed form solutions?
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  3. #3
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    Quote Originally Posted by wonderboy1953 View Post
    Are you only looking for closed form solutions?
    There are no closed form solutions to these equations.
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  4. #4
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    Hi,

    Thank you for your responses.

    I am afraid that my level of mathematical knowledge does not extend to closed form solutions.

    Are you saying that this equation cannot be solved without using graphs or trial and error ?

    Is the mathematics for closed form solutions too advanced to be shown in a few lines ?

    Regards,

    Zorrozac
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  5. #5
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    Well, there is/are solutions to the problem. Closed form means an explicit answer that involves a finite combination of elementary functions. For example, when you find the roots of a quadratic, you will get the answers in the form of square roots and fractions. However, there doesn't seem to be such a solution for the equations you have provided.

    In this case we have to resort to non-closed form solutions in the form of either an inexact answer, an infinite sum or the use of special non-elementary functions.
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  6. #6
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    So the answer to "can this simple equation be solved using logarithms alone?" is NO.

    Thanks to all who contributed, especially Vlasev.

    Best regards,

    Zorrozac
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