Hi @Chaitanya Kiran ,
Let me update my answer.
In SQL Server Availability Groups, taking a log backup on the primary replica does not automatically trigger a log backup on all secondary replicas. But its LSN will be updated, as you can see from the test in the link I posted earlier.
In an Availability Group configuration, each replica maintains its own independent transaction log, which is used for local recovery in case of a failover. When a log backup is taken on the primary replica, it only backs up the transaction log of the primary database on that primary replica.
However, you can configure secondary replicas to perform automatic backups using the "backup preferences" feature of the Availability Group. When backup preferences are configured, SQL Server can automatically take backups on secondary replicas based on the defined preferences.

It is important to note that the log backups taken on the secondary replicas are independent of the backups taken on the primary replica. However, all backups, including log backups taken on secondary replicas, can be used during a restore operation to bring a database up to the desired point in time.
Best regards,
Seeya
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