All logging adds a date and time stamp to the log; however, it is the plug-in's responsibility to identify itself in the log due to the multiple of plug-ins writing to the combined file.

With everything on the a same machine, all three executing programs can use the same log file, and you'd get a nice combined log.

Using a single combined log file makes it somewhat simpler to collect and scan data for anomalies when something happens, and to manage the growth and rotation of logs files.