The following code, inserted in your wp-config.php file, will log all errors, notices, and warnings to a file called debug.log in the wp-content directory. It will also hide the errors so they do not interrupt page generation.

// Enable WP_DEBUG mode
define( 'WP_DEBUG', true );

// Enable Debug logging to the /wp-content/debug.log file
define( 'WP_DEBUG_LOG', true );

// Disable display of errors and warnings
define( 'WP_DEBUG_DISPLAY', false );
@ini_set( 'display_errors', 0 );

// Use dev versions of core JS and CSS files (only needed if you are modifying these core files)
define( 'SCRIPT_DEBUG', true );

NOTE: You must insert this BEFORE /* That’s all, stop editing! Happy blogging. */ in the wp-config.php file.