As the evolution of smart phone, 3D graphics become more and more important in mobile computing systems. Within 3D graphics, logarithmic arithmetic is usually utilized to simplify multiplication, division, and power operations. In this paper, we propose a low-error and Rom-free logarithmic arithmetic unit for 3D graphics applications. The logarithmic arithmetic unit applies non-uniform regional linear interpolation and compensation method for logarithmic converters. According to experiment results, proposed 2-region logarithmic converter reduces 48.0% error range and 42.1% percent error. 21.6% area and 13.8% power consumption are gained.