Manual:$wgCheckUserLog

CheckUserLog is a variable that "points to" a file which will be used as a log for queries launched under the CheckUser extension. To set up a log:
 * 1) Install the checkuser extension, using the instructions at extension:CheckUser;
 * 2) Create a .txt file in the folder where the CheckUser extension files are: for example, in /extensions/CheckUser, create /extensions/CheckUser/CheckUser-log.txt;
 * 3) In LocalSettings.php, put $wgCheckUserLog = "$IP/extensions/CheckUser/CheckUser-log.txt";.

Your log should now be enabled.