You can use the Reuse Library to implement a reusable component that can display an application log.
For more information on how to use the Fiori reuse library in a freestyle app, see Freestyle App Integration.
For more information on how to use the Fiori reuse library in a Fiori elements app, see Fiori Elements Integration OData V2 (for OData V2 apps) and Fiori Elements Integration OData V4 (for OData V4 apps).