No, it's not possible. You can find that info on the BACKUP doc:
When you restore a backup created by BACKUP DATABASE (a data backup),
the entire backup is restored. Only a log backup can be restored to a
specific time or transaction within the backup.
This limitation will be clear by Understanding SQL Server Backup Types:
A full backup, as the name implies, backs up everything. [...] This is a complete copy, which
stores all the objects of the database: Tables, procedures, functions,
views, indexes etc. Having a full backup, you will be able to easily
restore a database in exactly the same form as it was at the time of
The log backup, as its name implies, backs up the transaction logs.
[...] A transaction log file stores a series of the logs that
provide the history of every modification of data, in a database.
As you can see, the full backup is just a copy of the whole database as it was at that moment whereas a log backup contains each transaction (individually logged like a step by step recipe) that happened since the last log backup.
The fact that you took log backups doesn't "upgrade" a full backup to be capable of doing a point in time recovery by itself if the log backup files were discarded afterwards. The log backups are still needed to perform a point in time recovery of the 40th day as you described.
Therefore, if you wanna be able to restore the 40th day using point in time recovery from now on, you should change your backup plan to keep enough log backups to cover that period.
To have a better understanding of the content of a log backup see During a log backup is the data backed up to the start or end of the operation?