Wikipedia says NF = 10 log ( SNRin / SNRout) = SNR in - SNR out. My question i guess is more mathematical relating to how SNRin - SNRout was derived.

Please advise.

 

You have misquoted Wikipedia slightly.

It actually says

The derivation would be in complete form

\(NF=10log\( \frac{SNR_{in}}{SNR_{out}}\)=10log(SNR_{in})-10log(SNR_{out})=SNR_{in,dB}-SNR_{out,dB}\)

remembering that in general

\(log(\frac{A}{B})=log(A)-log(B)\)

 

And the SNRin and SNRout figures are measurements, not derivations.