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A fundamental feature of the electromagnetic wave logs is the logging response (phase difference and amplitude ratio) dependent on the both dielectric constant and conductivity in general. We derived the response functions (RF) of the electromagnetic wave logs and proposed their fast algorithm based on an integral equation of electromagnetic field and a weak scattering approximation. Using the fast algorithm of RF in the inhomogenous, a fast algorithm of Jacobi matrix was to be advanced easily. A theoretical results about the response characteristics of phase difference and amplitude ratio were also gained. It was shown that the phase difference is sensitive to the conductivity within substantially the same volume as the amplitude ratio is sensitive to the dielectric constant, and the phase difference is sensitive to the dielectric constant within substantially the same volume as the amplitude ratio is sensitive to the conductivity, in the homogeneous medium.