Flooring Tile - Raising Floor Level for Ceramic Tile

I need to lay down tile for hearth for a wood burning stove. I have the floor stripped down to the slab. I need to raise it about 3/4" to make it level with the Pergo floor in the remainder of the room.
Here's my questions:

1. Can I used backer board? If so, how do I attach it to the slab?
2. If backer board is not the way, do I use thin set or regular cement to make up the 3/4"?
3. Is there any precautions I need to do so the tiles don't crack when I put extremely heavy wood stove in place?

thank in advance,

put the tile on the cement and use a transition moulding from pergo

1)No backer on a slab
2)No, thinset will crack if deeper than 3/8" and being very sticky makes it difficult to get it smooth. If you need to build up the area, Dam the perimeter of the area 1/4" around any side that does not meet the pergo and about 1" around the area that it will meet the laminate. 1/4" is needed for expansion around fixed objects like walls, 1" expansion gap is needed to alow for the laminate transitions to give you the required 1/4" gap at the end of the laminate for expansion, 1/4" gap at the end of the hearth area, and the 1/2" or so that the mounting strip for the laminate transition that gets attactched to the floor with a polyurethane ahesive or holes drilled with a hammer drill into the slab and plastic anchors inserted for screws to hold the mounting strip down. Fill the dammed off area with self leveling cement after priming the slab with self leveling cement primer.
3)Ensuring the tiles have 100% coverage under them and full support at the corners will prevent the point loads from the stove feet from cracking the tile. Also, do not use any premixed products to set you tile or to grout.