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Math Help - Solving a difficult n-th root equation

  1. #1
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    Solving a difficult n-th root equation

    How can I solve for n for something of this form?

    (1.14)^(1/n) - 1 = 0.13/n

    I managed to arrive at this:

    n[(1.14)^(1/n) -1] = 0.13
    But I don't know where to go from there.
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  2. #2
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    Quote Originally Posted by Volcanicrain View Post
    How can I solve for n for something of this form?

    (1.14)^(1/n) - 1 = 0.13/n

    I managed to arrive at this:

    n[(1.14)^(1/n) -1] = 0.13
    But I don't know where to go from there.
    I don't know a way to solve this equation algebraically.

    I would use Newton's method to get an approximate value for n:

    f(n)=n\left((1.14)^{\frac1n}-1\right)-0.13~,~n\in \mathbb{R}

    Solve f(n)=0 for n.

    I got n \approx -8.3045
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