How to increase volume of my turntable - pre-amp - amp setup

Hi. Good Day to you all! My first post and first visit.

I have a cheap Scott turntable equipped with a low priced Audio-Technica mm cartridge through a cheap Berhringer pre-amp into a Logitech Z-680 speaker system. I also have a CD player separately into the system.

The volume output from the speakers is markedly lower from records than from CDs. I suppose that CD medium might be a little louder (the loudness war thing?) than vinyl but this seems to be an output problem not a difference in mediums.

I would like to increase  LP volume. How can I do this? Can I get a higher output cartridge for my turntable? How about a pre-amp with higher output? The Logitech speaker system seems plenty powerful.

I've researched but can't seem to find an answer that I understand. 

Thanks!