Cluster logs can be observed directly on the cluster UI, under Driver logs, Spark logs related to the executors can be seen under the Spark UI section in the cluster configuration and under Executors, you can look for the stdout and the stderr 

For logs more related to events you can set up audit log delivery on an S3 bucket or by querying the system table s mentioned in docs https://docs.databricks.com/en/administration-guide/account-settings/audit-logs.html