• Pick a course with plenty of users and a few months history
• Set your php.ini memory_limit to something generous but sensible (I have 512M)
• Go to the logs report for the course and select everything (works fine, hundreds of pages are expected - the course I had bother with had 1,700 pages)
• Choose the download as CSV (or any other format) at the bottom of the page
• Download quickly fails having consumed all the memory (can't allocate x bytes error)

The code to achieve this seems surprisingly complicated for what it does but I can only assume that the report attempts to load the whole data structure into memory before passing it off to a library function for the actual download. This was never going to work due to the potential for large amounts of log data.