As Adam said said, logging is mostly outside of WebSharper. But just to share few ideas, with NLog (an other log framework I suppose), you can setup targets and rules to log into console outputs, files and even build custom targets.

I recently shared one of my favourite logging option: Having a logging live stream using HTTP SSE protocol with WebSharper sitelet.

The link is here.You could have a look if that's what you are looking for. Hope this helps.

Logging is mostly outside of WebSharper. For server-side logging, you can/should use any of the available logging frameworks, like log4net, Elmah, etc. For client-side logging, your best option is likely sending JS logs to a server.