How to Put Logs in Graphing Calculator

Basic Logarithm Graphing

Logarithmic functions have the general form y = logₐ(x), where 'a' is the base of the logarithm. The most common bases are 10 and the natural logarithm (ln) with base e ≈ 2.71828.

The graph of a logarithmic function will always pass through the point (1,0) because logₐ(1) = 0 for any valid base 'a'. The function will be increasing if a > 1 and decreasing if 0 < a < 1.

Key Properties of Logarithmic Functions

• Domain: x > 0
• Range: all real numbers
• Vertical asymptote at x = 0
• Horizontal asymptote at y = -∞ when a > 1
• Horizontal asymptote at y = ∞ when 0 < a < 1

Understanding these properties will help you interpret the graphs you create and verify that your calculator is displaying them correctly.

Using Your Calculator

Most graphing calculators have a built-in logarithmic function that you can use to graph these functions. Here's how to set it up:

Step 1: Access the Graphing Mode

Turn on your calculator and navigate to the graphing mode. This is typically found under the "Graph" or "Y=" menu.

Step 2: Enter the Logarithmic Function

In the Y= editor, enter your logarithmic function. For example, to graph y = log₁₀(x), you would enter:

Step 3: Set the Window

Adjust the window settings to get a good view of your graph. For logarithmic functions, you'll typically want:

• Xmin: 0.0001 (to avoid the vertical asymptote)
• Xmax: 10 (or another appropriate value based on your function)
• Ymin: -10
• Ymax: 10
• Xscl: 1
• Yscl: 1

Step 4: Graph the Function

Press the graph button to display your logarithmic function. You should see a curve that starts at the point (1,0) and increases or decreases depending on the base.

Step 5: Adjust as Needed

If your graph doesn't look right, try adjusting the window settings or checking that you entered the function correctly. Some calculators require you to specify the base explicitly, so you might need to enter Y₁ = log(X,10) instead of just Y₁ = log(X).

Worked Examples

Let's look at a couple of examples to see how this works in practice.

Example 1: Basic Logarithm

Graph y = log₁₀(x) using your calculator.

1. Enter Y₁ = log(X) in the Y= editor
2. Set the window as described above
3. Press GRAPH

You should see a curve that starts at (1,0) and increases as x increases. The graph will be concave down, showing the decreasing rate of growth as x increases.

Example 2: Different Base

Graph y = log₂(x) using your calculator.

1. Enter Y₁ = log(X,2) in the Y= editor (some calculators require the base to be specified)
2. Set the window as described above
3. Press GRAPH

You should see a curve that starts at (1,0) and increases as x increases. This time, the curve will be steeper than the base 10 logarithm because the base is smaller.

Common Issues

When graphing logarithmic functions, you might encounter some common problems. Here are solutions to these issues:

1. Graph Doesn't Appear

If your graph doesn't appear, first check that you've entered the function correctly. Make sure you're in the right mode (Graph vs. Table vs. Y=). Also verify that the function is turned on (some calculators require you to enable each Y= function separately).

2. Graph Looks Wrong

If your graph looks distorted or incorrect, try adjusting the window settings. For logarithmic functions, you typically want Xmin to be a small positive number (like 0.0001) to avoid the vertical asymptote at x=0.

3. Calculator Doesn't Recognize "log"

Some calculators use different notation for logarithms. If your calculator doesn't recognize "log", try using "LOG" or check the documentation to see what function name it uses for base 10 logarithms.

4. Graph is Too Small

If your graph is too small to see clearly, adjust the window settings. You might need to zoom in by making Xmax smaller or zoom out by making Xmax larger. The Ymin and Ymax settings can also affect how much of the graph is visible.