The area under the 1/x curve and the ln function

Use the slider bar to move the right hand border of the region under the graph y=1/x. If Area(a) represents the area under the curve between x=1 and x=a, what do you notice about the values Area(2) + Area(3)? 3 x Area(2) ? 2 x Area(3)? Area(2) + Area(5)? What is the value of a for which Area(a)=1?

How does all this suggest that Area(a) = ln a?