Request logging should be done in a structured form. You don't need an indexing solution for this kind of request logging - It's vaguely timestamp ordered, and that's about it. If you need to search it, it gets loaded into a structured data query engine - Spark, or Bigquery/Athena.
Audit logging belongs in a durable database and it requires being written and committed before the request is finished serving - Logging frameworks that dump to disk or stdout obviously fail his requirement.