# The log transformation of a Rayleigh distribution, or identifying the following distributions

I have a set of data which is recorded in a $$\log_{10}$$ scale. To be exact it is $$dBV_{pk} = 20\log_{10}(V_{pk})$$ units. If I plot the distribution of the logged data as a PDF I get the following:

If I then linearise this data, so $$10^{dBV_{pk}/20}$$, and again plot the distribution I get the following:

To me this looks very much like the Rayleigh distribution -- it could be something else, but that is my best guess so far.

My question is: Given that the linear data is a Rayleigh distribution -- what is the $$log_{10}$$ transformation of a Rayleigh distribution? Or can anyone identify the distribution of the first plot (the original logged data)? If either is answered it automatically gives me the other.