They're required to be public services. https://crt.sh/monitored-logs is the list of logs monitored by crt.sh (a public log monitor operated by Sectigo, a commercial CA) if that helps. Each of the major browsers also publishes which logs they trust and provides information about e.g. distrust of logs. Is the problem that you couldn't figure out how to use a log? It doesn't just have a web site where you can type in searches you need to be able to use their web API as defined in the protocol documentation.