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This paper provides an analysis of a log detector in order to determine its response to a multitone input for detection of spurious emissions in a radio frequency transmitter. Treatment is given to the single tone response of the log detector and extended to a two-tone log detector system, where a large signal and a small signal are present. The large signal is observed to experience logarithmic processing with an output at zero frequency. The small signal produces an output at the difference frequency of the large signal frequency and small signal frequency that is approximately proportional to the ratio of the small signal voltage to the large signal voltage. The two-tone results are generalized to an m-tone input. Experimental results are presented to show the accuracy of the model. The log detector circuit analyzed is able to detect a spurious emission within 45 MHz of the main signal with plusmn1 dB of accuracy.