RegionPlot[{y<=Log[Floor[x]],y<=Log[x],y<=Log[Ceiling[x]]},{x,1,10},{y,0,Log[10]}]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.