As far as I know, for a text file like a .log, it will be up to some sort of configuration in your web browser or whatever else you use to view the log files to determine what encoding it will choose to display. In the other situation, I was able to specify UTF-8 for the web pages, but the logs aren't (and aren't intended to be) HTML-based web pages.
All that said, if you open a log file in a program that understands encodings, it should look fine. I will admit, however, that I have not tried to do so.