you can do one of two things
- wait for the logging rewrite to go through which would log to disk as well (so you don't have to do anything)
- right click the app and open the app as a folder. go deeper into the folder until you find the citra-qt file next to the citra-qt-bin file. you can edit the citra-qt file with a text editor and in there you should see
cd "\`dirname "\$0"\`"
chmod +x citra-qt-bin
open citra-qt-bin --args "\$@"
change the last line to be
open citra-qt-bin --args "\$@" 2>~/citra-log.txt
then when you launch the citra app it should write to citra-log.txt instead inside your homefolder. (note i don't have access to a mac any more so i can't test it)