This paper presents an efficient ASIC implementation for the hardware approximation of the logarithm function which can be used for emerging high dynamic range image processing applications. By employing a new logarithm approximation method, the modified barrel shifter circuit and optimized leading one detector and encoder, the proposed approach can reduce the hardware area and improve the logarithm computation speed significantly while achieve the similar accuracy compared with other methods. The implementation results in 0.18-μm CMOS technology are also presented and discussed.