how can i put tile in my bathroom using thin cement board.so my bathroom floor can be even with my living room floor.
You have to consider the thresh hold-doorway. Usually it is a strip of marble. The bathroom is considered a wet area so you may not want it even with your living room floor. Blue board is most often the foundation for good tile work.
Use a product called Schlueter Ditra. Most tile installers should know about it. It is a special tile underlayment that is about 1/8 thick and stuck with thinset mortar to your floor be it cement or a wood subfloor. Should be able to purchase it from anyone that sells ceramic tile.
I guess I've been on the planet Mars far too long? Blue Board?? On a floor? Tile underlayment?? I tile every day of my life, even ceilings, and never heard of either method suggested. Not knowing at all your current bathroom substrate, or the substance of the LV room floor, NO you cannot find concrete backer board thinner than 1/4. In fact I suspect you'd have a hard time finding the 1/4. 1/2 is standard. I wonder what finish the Bathroom floor is currently? Certainly the Marble strip for a transition is also standard, often between tile and tile. There are transition moldings sold for the purpose of going fom tile to carpet, or tile to hardwood, even pancake, overlaps. Steven Wolf Just my two sense