Years ago, I tried "inotify" on a kindle, but it was mostly useless. Files changed without detection. Not sure if there is a reliable way other than to see if the logfile timestamp or size has changed, by periodic polling. Though you could try inotify again (but it may require linux kernel support). Others have discussed this issue as well:
How to notice log file changes with Linux standard tools?
In Linux, how do I run a shell script when a file or directory changes
https://en.wikipedia.org/wiki/Inotify
Like I said,
inotify did not work for me (but that was years ago), so tools based on inotify are likely to be unreliable too.
YMMV