Polar Plots with Exclusions

p=Table[PolarPlot[{Sin[x]Log[Floor[x+1]],Sin[x]Log[x+1]},
{x,k*Pi/2,(k+1)*Pi/2},
PlotStyle->Hue[k/16]],{k,Range[0,15,1]}];
Show[p,ImageSize->Large,GridLines->Automatic]