The problem is as such:

5*3^{x}>12*5^{x}

I have been mulling over this thing for quite some time now. Normally I would start by dividing both sides by the 5, but that doesnt isolate the x, so that doesnt seem to be the way to go. So I turned everything into logs.

log 5 + x log 3 > log 12 + x log 5

From here, I have tried just about everything I could come up with. Subtract around so that you get the x logs on one side, and the non-variable logs on the other side, but then they dont seem to match up. Can someone let me know where I go from here? I am sketchy on what is allowed with this. Can I simply have x log 3 - x log 5, and combine them somehow, even though one is a log 3, and the other is a log 5? I feel like my head is swimming from all the conversions back and forth between log and not log formats.