In this paper, high-order Taylor Series expansion is proposed to explore the most effective formulas of log-spectral compensation. The power feature, which is crucial to speech recognition in noisy environments and can't be compensated in usual feature compensation, is processed similarly to spectral subtraction. The modeling accuracy of speech log-spectral Gaussian Mixture Model (GMM) is also discussed and carefully treated. Experimental results show that the log-spectral compensation can greatly improve recognition performance in noisy environments and with the acoustic model trained using multi-condition data, the recognition performance is superior to that in matched conditions.