Can you add the links you are referring to? Because just mirroring does not need a log. A log (on the same or extra device) is usually involved when you use a journaling filesystem - if you use mirroring or not on the layer below (i.e. the blocklayer).
Update: Ok, with the links things are clearer now. The LVM mirroring seems to be quite different from the linux md (RAID 1) mirroring.
To quote from the lvcreate man page:
Specifying the optional argument "--corelog" will create a mirror with an in-memory log verses a disk-based (persistent) log. While this removes the need for an extra log device and may be slightly faster, it requires that the entire mirror be resynchronized upon each instantiation (e.g. a reboot).
Thus, with a memory based log you get a significant performance hit at startup and a performance hit, when the log physical volume is on the same hardware disk.
Googling around, mirroring using Linux
mdadm seems to be the better approach ATM. (You can use the md device as physical device for some lvm setup.)
First, it does not need an extra log (and does not do an expensinve resync at every startup).
Second, lvm mirrors does not seem to support parallel reading, i.e. md mirrors should have better read performance: