You can also view the log file the next time you start DS by going to the menu bar and selecting
Help > Troubleshooting > View Log File…
In Windows, after the log file opens in Wordpad, you can also select File > Save As, then instead of saving, just drag a shortcut from log.txt in that window to your desktop or wherever for later use as a fast way to locate the file.
Note that sometimes things aren’t written to the log file until you exit DS though, so if it is appropriate to do so, you may want to exit first and then look.
If it exited normally, the last line of the file should look something like this:
———————- DAZ Studio 220.127.116.11 exited—————————
If that’s not the last line, I would assume it crashed or was otherwise unexpectedly terminated.
Note that sometimes crashes pop up a big window that stays, and sometimes they just give a tiny brief message that goes away right away that’s easy to miss.
EDITED TO ADD: If you are running out of memory, you might want to make a point of saving prior to rendering so you won’t loose anything if the render proves too be too much, then also exiting/restarting to clear the undo to try to free up a tiny bit more memory. I was recently working on a scene on my 32-bit PC that kept getting memory errors and crashes more and more often the more I added things to it to the point where I couldn’t spot render without crashing. I was almost done, and just needed to add one more thing to the scene. I ended up running TextureAtlas one a distant background figure to cram all it’s textures together and then made them much smaller in a desperate attempt to use less memory; it worked, and I was finally able to add the final item to the scene and render without the crash. Depending on what you are doing and how close you are to your PC’s memory limit, a workaround like this might allow you to get your scene done. (Of course your problem could turn out to be something different too.)