There was discussion earlier this year about creating a design doc for OpenCensus to handle logs. I'm not sure if that got finished, or it was sidelined while the OpenCensus & OpenTracing merger was worked on. Both projects will combine under the OpenTelemetry name.
I've been quite happy with the OpenCensus instrumentation SDKs.
I think the Logs & Metrics space is interesting, especially because there is so much overlap, both are just ways of representing data about an event that occurred in the software.
OpenCensus is fairly widely backed: Google, Microsoft, Etsy, Scalyr...[1]
[0] https://github.com/census-instrumentation/opencensus-service...