DB Syncing issues are back: where can I find the log on MAC?

Dear all,

Following some problems with library syncing, I decided to create a new network volume on top of the first one that was getting too big.
On the new network volume, I discovered that adding new files using the Finder while AS was up and running, immediately triggers a scan but limited to the new files: that was impressively fast!
I decided to give it a try on the old network volume (whose size has been reduced by transferring some files). It did not work as expected: it run during hours, without any visible progress, and AS crashes. I restarted the whole process two times: it lasted during more than 10 hours and crashed.
This is pretty strange as I managed to synchronise it in less than 5 hours before, with a larger number of files.
Can someone tell me where I could find the log information on Mac, as I did not see anything particular on console.

Thanks.

CPU usage of AS is rather low (around 10%) and I do not hear much disk activity neither.
In addition, I saw two errors this morning:
cannot open file at line 43354 of [378230ae7f]
os_unix.c:43354: (2) open(/var/db/DetachedSignatures) - No such file or directory

I rebooted my Mac Mini just after this and so far the error did not pop up again. But there are no clear signs of any progress