Interpolation-based reversible data hiding (IRDH) is a method for embedding data in a reversible manner into digital images. It is based on the polynomial interpolation to hide the secret data bit stream in the coefficients of the interpolation polynomial. In this paper, an IRDH method that combines a modified neighbor mean interpolation is presented with a new method for reversibly embedding secret data in interpolated pixels. This method uses log base 2 of the decimal value of the interpolated pixel to replace a corresponding number of bits with the bits of the secret data, allowing for a higher bit stream to be embedded with better image quality. The results from experiments show that the introduced method can implant on average, 1300000 bits of secret data with an average PSNR of 28.5 dB, which is a significant improvement over existing and related works.