As Exchange Administrator it would be bad day if you have exchagne database in Dirty Shutdown State and you dont have required log files to perform soft recovery. Below link has a steps on how to perform soft recovery if you have al the require log file.
If you dont have the required log files then you have to follow below steps to recover the database
1. Run ESEUTIL /P database_filename.edb (from the BIN folder and repair the edb files)
2. Delete the log and chk files.
3. Run eseutil /d database_filename.edb (Defrag the Database)
4. Run isinteg (isinteg -s servername -fix -test alltests) from the bin folder.
5. Mount the stores
Eseutil and Isinteg would be really long time , depending on the size of the database. Microsoft always recommends to keep the database size less then 100 GB. If you are using CCR environment then it can grow more then 100 GB as you will be multipe copies of the log files for recovery purpose