From the 'Help' menu, select 'About LI-Capture':

In the bottom left corner of the about screen, click the 'Explore .ini and log files' button:

This will open the LI-Capture folder on your computer that contains the log files. The filename of a log file can be 'li-capture.log' or 'li-capture.log.x' where x is a number.

When asked to send log files for support purposes, it is recommended to send all log files that are available.