Generally quite a lot of us would have used the script command. This generates the logs for the session. But the problem with the logs is that it contains a lot of un-readable characters. These characters are mostly from the color codes, and as such can be removed very easily with a single command:
cat typescript | perl -pe 's/e([^]|[.*.*?[a-zA-Z]|].*?a)//g' | col -b > typescript-processed
This assumes the input log file is named as typescript and the output is kept as typescript-processed. You can change the names as required.