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High Quality Content by WIKIPEDIA articles! Zech's logarithms are used with finite fields to reduce a high-degree polynomial that is not in the field to an element in the field (thus having a lower degree). Unlike the traditional logarithm, the Zech's logarithm of a polynomial provides an equivalence it does not alter the value.Zech logarithms are also called Jacobi Logarithm (see. e.g. Lidl,Niederreiter, Finite Fields, Cambridge University Press, 1984), after Jacobi who used them for number theoretic investigations (C.G.J.Jacoby, "Uber die Kreistheilung und ihre Anwendung auf die Zahlentheorie, in Gesammelte Werke, Vol.6, pp. 254-274).