Solid Hardwood, Engineered and Laminate Flooring - plywood on concrete slab?

I want to carpet over a room that is partially covered with a hardwood floor. Under the hardwood floor is concrete slab. I need to raise the level of the portion of the room that does not have the hardwood flooring to match the portion that is covered with hardwood flooring. I am thinking that I could use plywood of the same thickness to avoid the cost of laying more hardwood. How is plywood installed on concrete slab? If you use glue - what kind? Can you use some type of fastener? Is this the right solution to this problem?

You need to go rent a concrete nailer. It shoots a nail through the plywood into the concrete. The concrete nail gun is literally a gun. It uses .22 calibur shells to fire the nail. I just did 700 sq. ft. of plywood over concrete last week and it worked pretty well. The kickback of the gun hurts your hands so you might want some padded gloves handy. GOOD LUCK!