The ULS logs are located on and Exchange 2013 and Exchange 2016 server located at :C:\Program Files\Microsoft\Exchange Server\V15\Bin\Search\Ceres\Diagnostics\Logs. These logs contain vital information about the health of the search indexer as well and the health of the search requests on your Exchange server.
The logs are text and you can parse them with your favorite parsing tool but we also have a tool called ULSViewer which allows for filtering and formatting of an entire set of log files. Very cool tool. You can find it located at https://www.microsoft.com/en-us/download/details.aspx?id=44020