Put Log in Graphing Calculator

Graphing logarithmic functions in a calculator is essential for understanding exponential growth, decay, and other mathematical relationships. This guide explains how to input and visualize logarithmic functions in common graphing calculators, with step-by-step instructions and practical examples.

How to Put Log in a Graphing Calculator

Most graphing calculators support logarithmic functions through the LOG or LN functions. Here's how to enter them:

Common Logarithm (Base 10): LOG(100) = 2

Natural Logarithm (Base e): LN(e²) ≈ 2

Step-by-Step Instructions

Turn on your graphing calculator and clear any existing functions.
Press the Y= button to access the function editor.
Enter your logarithmic function using either:
- LOG(X) for common logarithm (base 10)
- LN(X) for natural logarithm (base e)
Set the window parameters (Xmin, Xmax, Ymin, Ymax) to appropriate values for your function.
Press GRAPH to display the logarithmic curve.

Tip: For better visualization, adjust the window settings to show the full range of your logarithmic function. Common logarithm (LOG) is typically used for base 10 calculations, while natural logarithm (LN) is used for base e calculations.

Common Logarithm (Base 10)

The common logarithm, denoted as LOG, uses base 10. It's widely used in science, engineering, and finance for calculations involving powers of 10.

Example Calculation

Let's graph LOG(X) from X=0.1 to X=100:

Y1 = LOG(X)

Window settings:

Xmin = 0.1
Xmax = 100
Ymin = -2
Ymax = 2

The graph will show a curve that passes through (1,0), (10,1), and (100,2), demonstrating the logarithmic relationship where each step on the x-axis represents a power of 10.

Natural Logarithm (Base e)

The natural logarithm, denoted as LN, uses Euler's number (e ≈ 2.71828) as its base. It's fundamental in calculus and exponential growth/decay models.

Example Calculation

Let's graph LN(X) from X=0.1 to X=10:

Y1 = LN(X)

Window settings:

Xmin = 0.1
Xmax = 10
Ymin = -2
Ymax = 2

The graph will show a curve that passes through (1,0), (e≈2.718,1), and (e²≈7.389,2), illustrating the natural logarithmic relationship.

Logarithm Properties

Understanding these properties helps in working with logarithmic functions:

Product Rule: LOG(ab) = LOG(a) + LOG(b)
Quotient Rule: LOG(a/b) = LOG(a) - LOG(b)
Power Rule: LOG(aⁿ) = n*LOG(a)
Change of Base: LOGₐ(b) = LOG(b)/LOG(a)

These properties are automatically applied by most graphing calculators when you enter logarithmic expressions.

Troubleshooting

If your logarithmic graph doesn't display correctly, try these solutions:

Check your function syntax: Ensure you're using LOG(X) or LN(X) with proper parentheses.
Adjust window settings: For LOG(X), try Xmin=0.1, Xmax=100, Ymin=-2, Ymax=2.
Clear old functions: Press CLEAR or DEL to remove previous entries.
Check calculator mode: Ensure it's in degree or radian mode as needed.

Note: Some calculators may use "log" instead of "LOG" or "ln" instead of "LN". Refer to your calculator's manual for the correct syntax.

FAQ

What is the difference between LOG and LN?: LOG uses base 10, while LN uses base e (approximately 2.71828). LOG is common in everyday calculations, while LN is used in advanced mathematics and calculus.
How do I graph a logarithmic function with a different base?: Use the change of base formula: LOGₐ(b) = LOG(b)/LOG(a). For example, to graph base 2 logarithm, enter LOG(X)/LOG(2).
Why does my logarithmic graph show a vertical asymptote?: Logarithmic functions approach negative infinity as X approaches 0 from the right. Adjust your Xmin setting to a small positive value (like 0.1) to avoid this.
Can I graph logarithmic inequalities?: Most graphing calculators can't directly graph inequalities, but you can graph the functions and use test points to determine the solution region.
How do I save logarithmic graphs for reports?: Use the PRINT or SAVE function on your calculator, then transfer the image to your computer or print it directly.