Studies of contrast sensitivity of the human eyes show that logarithmic curves obey the Weber-Fechner law of just noticeable difference response in human perception. In this paper, we propose a local contrast enhancement algorithm with logarithm-based curves for both high dynamic and low dynamic images and this algorithm can adaptively change the curvature with local information. We also define two parameters to decide the level of contrast enhancement in the tone mapping procedure. For halo artifact which is suffered from local operator, a two-stage procedure is designed to solve the problem. We present experimental results to show performance of our algorithm compared with other existing methods.