Using FFT for spectral analysis: How to convert from power to dBm?

I have the output of my FFT, an array of complex numbers, and each one has been computed to the magnitude squared. To my understanding, the magnitude squared is equivalent to the power, so in order to map to dBm, I would take 10 * log(x) of each of these numbers. This does not seem to give accurate dBm levels according to another spectral analyzer.

Converting to magnitude voltage, by taking the square root of the magnitude squared and dividing by the size of the FFT, and then taking the 20 * log(x) of this number seems to give closer dBm level when compared to other equipment. Why is this?