Transaction Log Backup job failed

Our backup log job failed with following error: 

Executed the below query: 

"BACKUP LOG [DemoData] TO  DISK = N'C:\Backup\xxx\xxx_backup_a.trn' WITH NOFORMAT, NOINIT,  NAME = N'xxx_backup_a', SKIP, REWIND, NOUNLOAD,  STATS = 10 "

and it failed with the following error: "BACKUP LOG cannot be performed because there is no current database backup. BACKUP LOG is terminating abnormally.". Possible failure reasons: Problems with the query, "ResultSet" property not set correctly, parameters not set correctly, or connection not established correctly. 

Here as error stated, the log backup job is failed as there is no FULL backup exists, in this 
situation, we might be having FULL backup for ALL DATABASES schedule to run weekly, and Transaction log backup for ALL DATABASES is scheduled to run daily. Here user creates the database dynamically or randomly in the middle of the week so FULL backup does not exists which cause give error.

There is no easy way to handle such situation but for safer side we can follow standards 

• Make a note for when are we creating database and whenever we creates database make sure to run full backup job for them. 
• Make the maintenance plan static and select particular databases only instead of ALL USER DATABASE.