The documentation for the Logging API - REST should describe / mention the parameters for both the message and exception. It behaves that the exception item is optional.
Below is from the docs sample request body which is the only mention of the exception
[ { “log-level”: DEBUG | INFO | TRACE | WARN | ERROR | FATAL, “logger”:value, “timestamp”:value, “message”: message-text-value, “exception”:error-text-value }]