When casting Genetic Engineering, the combat log is just.. bla bla Genetic Engineering.. It would be cool if combat log actually informed the player what attachments were generated. It could look something like this: Genetic Engineering provides "Troll Regeneration" Genetic Engineering provides "Altruism" Genetic Engineering provides "Crusher"
I feel the same about seeing what exactly a Purge removed because it can be hard to keep track of when there's so many attachments flying around everywhere from so many sources, so you could extend this addition to the battle log by mentioning all cases of cards being attached or unattached to a character. That said, I already find navigating the battle log difficult as it is now and only really do it to check whether a Wizard discarded Volcano in QD, so maybe adding even more information to it would only make it feel more cluttered.
If you're really curious about what a recent action attached or removed, can you f2 to look in the console? Battle log is not supposed to be comprehensive—it's an overview.