UPDATE `table_1` SET `key_1` = 'val_1' WHERE `key_2` = (SELECT `val_2` FROM `table_2` WHERE `key_3` = 'val_3' LIMIT 1) LIMIT 1
UPDATE `table_1` SET `key_1` = (SELECT `val_2` FROM `table_2` WHERE `key_3` = 'val_3' LIMIT 1) WHERE `key_2` = 'val_1'
UPDATE `table_1` SET `key_1` = 'val_1' WHERE `key_2` IN (SELECT `val_2` FROM `table_2` WHERE `key_3` = 'val_3')