I believe it all depends how your "log infrastructure" looks like,
if you're using CLM (Log Server) there are options for making that simpified
if your logs ends on SMS server - I don't think you can search few ELG files at the same time if I'm not mistaken (unless the script is already known to our belowed CCSM's here )
if your log switching is done per "size" on your Management Server (SMS) then obviously it must be a pain (and it is for each and everyone I guess) including myself to go trouch all the logs in order to find interesting record however, as Norbert mentioned in R80.10 for instance it should "per indexing" at least show you a snip of the record you're lookinig for. IMHO CLM is the best option, unless your logging facility does not need 12 months of log retention ...