It's not clear to me which RStudio product you are using. At first I thought this is probably RStudio Server Pro, but the fact you're using PostGres indicates that perhaps you are talking about RStudio Connect.
As far as I can tell, neither of these products store log files by default in the location you mention. You can find the default locations and how to change these in the respective admin guides, at http://docs.rstudio.com/ide/server-pro/ and http://docs.rstudio.com/connect/admin/.
I would have suggested that you post the contents of the Connect configuration file,
/etc/rstudio-connect/rstudio-connect.gcfg, but this is likely to contain some confidential information.
So, I can suggest the following options: