Advantages of log 2 normalized as compared to log 10 normalized
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If you use log-transformed expression (or concentration) values, you model PROPORTIONAL chances rather than additive changes. This is typically biologically more relevant.
Also the errors are usually proportional to the values (-> the variance is not independent from the mean -> heteroscedasticity). This kind of mean-variance relationship is usually absent on the log scale.
Apart from there merely phenomenological reasons there is some theoretical foundation for taking the logarithms, as for instance derived in this paper
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