cement board to replace 2nd layer of plywood


After removing the wall on the jacuzzi, I have a better idea of what the floor is really composed of. It looks like there is a 12/16" or 13/16" plywood over the joists, then there is 8/16" or 9/16" plywood over the first layer.
The second layer is more or less level with the carpeting in the master bedroom. I would like to keep the master bathroom as close to level as I can with the master bedroom level. If I put 1/4" or 1/2" cement board on top of the 2nd layer of plywood, I think the change will be sore to look at and will be a tripping hazard
Can the second layer or plywood be replaced with 1/2" cement board?
Some research on the internet makes me think that it will not be a problem for ceramic tile surface cracks.
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snipped-for-privacy@gmail.com wrote:

One thing to keep in mind is the larger tile you use, the stiffer your floor needs to be. Whoever remodeled my bathroom did not keep this in mind, and laid 6" tile on a floor that undoubtedly originally had the 1940's style little tiny mosaic tiles on it. There's several cracked tiles in the area of the can, although I think the remodel was likely done back in the 1980s.
nate
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When I did this, I added 3/4" plywood under the subfloor spanning the space between the joists to provide the needed stiffness. 2x4s glued to the joists and the extra plywood, plus lots of screws hold it all together. Tile places seem to usually recommend at least 1 1/4" of wood under the backer board.
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