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Computations in logarithmic number systems require realisations of four different elementary functions. In the current paper the authors use a recently proposed approximation method based on weighted sums of bit-products to realise these functions. It is shown that the considered method can be used to efficiently realise the different functions. Furthermore, a transformation is proposed to improve the results for functions with logarithmic characteristics. Implementation results shows that significant savings in area and power can be obtained using optimisation techniques.