Graphing Logarithmic Functions

Example

Graph y = log₂x.

Solution

Step 1 Rewrite y = log2x in exponential form. Step 2 Switch x and y. Step 3 Calculate ordered pairs.	x = 2y y = 2x
x y = 2x (x, y) -4 -1 0 y = 20 = 1 (0, 1) 1 y = 21 = 2 (1, 2) 2 y = 22 = 4 (2, 4) 4 y = 24 = 16 (4, 16)

Step 4 Exchange the x- and y- coordinates.

The new coordinates are (4, 2), and (16, 4).

Step 5 Graph the new ordered pairs.

Notice that the graph of y = log₂x is the reflection about the line y = x of y = 2^x.