Textbook Problem

Let $b>1$ .

a. Use the fact that $u={\log }_{b}v\iff v=b^u$ to show that a point (u, v) lies on the graph of the logarithinic function with base b if, and only if, (v, u) lies on the graph of the exponential function with base b.

b. Plot several pairs of points of the form (u, v) and (v, u) on a coordinate system. Describe the geometric relationship between the locations of the points in each pair.

c. Draw the graphs of $y={\log }_{2}x$and $y=2^x$ . Describe the geometric relationship between these graphs.