Rscript log file with input, errors and output

Is there a way to fully register (stdin, stdout, stderror) an R session running through Rscript in batch mode?

I know what I can use R CMD BATCHto register a full batch job session. I also know how to write errors and output to a log file using Rscript, but since it is often said that it R CMD BATCHis relic from the old days and needs to be used Rscript, I was wondering if it can also write everything,

I suppose this is not possible, but I'm not sure - and I don't know why.