Logs are very much not a time series so storing them in a time series database is not something that I would recommend. Time series are essentially a sequence of numeric data points in chronological order. Though events are usually in chronological order, they're not numeric data points (though they can contain that too).

As a consequence of being two different things, storing and analysing them efficiently need different solutions. I've seen people stuff everything in Elastic Search and it's certainly possible if you really want to.