Graphing Logarithmic Functions

To draw the graph of a logarithmic function, we can follow a three-step process.

1. Identify the base.
2. Determine points on the graph.
3. Plot the points and sketch the graph.

Let's do it!

Identifying the Base

Looking at the given function, we can see that the base is $b=2.$ $$\begin{array}{c}f(x)={\log }_2(2x)\end{array}$$

Determining Points on the Graph

Using the base, we will construct a table of values.

Plotting the Points and Sketch the Graph

Let's plot the points $(\frac{1}{4},\text{-}1),$ $(\frac{1}{2},0),$ $(1,1),$ and $(2,2),$ and connect them with a smooth curve.