So most servers do error logging but if you want to improve this functionality you can modify your wp-config.php file with the following code snippet. It consolidates not only the PHP errors but also logs any WordPress bugs that get reported via WordPress debugging being turned on.
// Enable debugging
// Log all errors to a text file located at /wp-content/debug.log
// Don’t display error messages write them to the log file /wp-content/debug.log
// Ensure all PHP errors are written to the log file and not displayed on screen