The log cannot be rebuilt because there were open transactions/users when the database was shutdown, no checkpoint occurred to the database, or the database was read-only. This error could occur if the transaction log file was manually deleted or lost due to a hardware or environment failure.

 One of our database was in recovery mode because of transaction log size exceeded the free space available and transaction was incomplete.

We performed the following statements to get it in working state though not recommended approach.

ALTER DATABASE DB_name SET EMERGENCY;
GO
ALTER DATABASE DB_name SET SINGLE_USER;
Go
DBCC CHECKDB (DB_name, REPAIR_ALLOW_DATA_LOSS) WITH NO_INFOMSGS, ALL_ERRORMSGS;
GO
ALTER DATABASE DB_name SET ONLINE
go
ALTER DATABASE DB_name SET MULTI_USER;

Hope it helps