I understand the 0.5m square cross-section to mean that the side of the square cross-section is 0.5m, making its area 0.25m2. Volume of the log=3×0.25m3=0.75m3. Relative density is based on the density of freshwater (1000kg/m3), so the density of the log is 810kg/m3, and its mass is 0.75×810=607.5kg. It displaces 607.5kg of water (which counterbalances its weight). This I understand to be the displacement. Density of water=1000=mass/volume, so 607.5kg has a volume of 607.5/1000=0.6075m3.
The base area of the log is 3×0.5=1.5m2, therefore the water level is 0.6075/1.5=0.405m above the base of the log. The centre of buoyancy (COB) is the centre of gravity (COG) of the displacement volume which is half this distance=0.2025m.
The COG of the log (when not immersed in water) is half its height, that is, 0.5/2=0.25m. The distance between the COG and COB=0.25-0.2025=0.0475m=4.75cm.
CORRECTION
I discovered a typing error in one of the calculations and I was using the wrong criteria for measuring the COB. These errors are now corrected.