This paper presents a high accuracy Mitchell-based logarithmic conversion algorithm suitable for integrated circuit implementation. A novel technique named range mapping is proposed to compress the range of approximation to one-quarter of that of the Mitchell's fraction, m. A 3-region piecewise linear approximation is then applied on the compressed range. Simulation results show that the proposed algorithm achieves both low absolute error and percentage error of 0.0037999 and 0.064002% respectively.