This problem can be solved by using the Archimedes Principle. The principle basically lets us derive a force balance between the weight of the log and the buoyant force exerted by the water, that is
weight of log = buoyant force exerted by water
simplification of the derviation would yield,
Dl/Dw = fraction of the of the log submerged in water = (1-0.25) = 0.75
where Dl = density of the log
Dw = density of the water (1000 kg/m3)
therefore Dl = 750 kg/m^3
Hope this helps
