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Note, that if we take logarithms at both sides of the equation, i.e. log[f(x)] = log(a)−b log(x), f(x) becomes a lineal function of x with a slope equal to −b.
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The numerator is a parabolic function having two analytically well defined crossing points (ξ+>0 and ξ−<0 ) with the horizontal axis given by
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CEO of Professional Science Editing for Scientists @ prosciediting.com