"The transaction log for database is full due to 'LOG_BACKUP'" in a shared host

In Addition to Ben's Answer, You can try Below Queries as per your need

USE {database-name};  
GO  
-- Truncate the log by changing the database recovery model to SIMPLE.  
ALTER DATABASE {database-name}
SET RECOVERY SIMPLE;  
GO  
-- Shrink the truncated log file to 1 MB.  
DBCC SHRINKFILE ({database-file-name}, 1);  
GO  
-- Reset the database recovery model.  
ALTER DATABASE {database-name}
SET RECOVERY FULL;  
GO 

Update Credit @cema-sp

To find database file names use below query

select * from sys.database_files;

Call your hosting company and either have them set up regular log backups or set the recovery model to simple. I'm sure you know what informs the choice, but I'll be explicit anyway. Set the recovery model to full if you need the ability to restore to an arbitrary point in time. Either way the database is misconfigured as is.