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Put Log Base Into Calculator Ti-83

Reviewed by Calculator Editorial Team

Calculating logarithms with custom bases on your TI-83 calculator is straightforward once you understand the proper syntax. This guide will walk you through the process step-by-step, explain the underlying formula, and provide practical examples to ensure you get accurate results every time.

How to Enter Log Base on TI-83

To calculate a logarithm with a custom base on your TI-83 calculator, follow these steps:

  1. Press the 2ND key and then the MATH key to access the math menu.
  2. Scroll down to option 3: logBASE and press ENTER.
  3. Enter the argument (the number you want to find the logarithm of).
  4. Press the comma key (,).
  5. Enter the base of the logarithm.
  6. Press ENTER to see the result.

Pro Tip

Remember that the base must be a positive number and cannot be equal to 1. The TI-83 will display an error if you try to use an invalid base.

Formula Explanation

The logarithm with a custom base is calculated using the change of base formula:

Logarithm with Custom Base Formula

logb(a) = ln(a) / ln(b)

Where:

  • a is the argument (the number you're taking the logarithm of)
  • b is the base of the logarithm
  • ln represents the natural logarithm (logarithm with base e)

This formula allows you to calculate logarithms with any positive base using the natural logarithm function, which is available on most scientific calculators including the TI-83.

Example Calculation

Let's calculate log5(25) using the TI-83:

  1. Press 2ND then MATH to access the math menu.
  2. Select 3: logBASE and press ENTER.
  3. Enter 25 (the argument).
  4. Press the comma key (,).
  5. Enter 5 (the base).
  6. Press ENTER.

The calculator will display 2, which is correct because 5² = 25.

Result

2

This means that 5 raised to the power of 2 equals 25.

Common Mistakes

When working with logarithms on your TI-83, be aware of these common pitfalls:

  • Using a base of 1: The TI-83 will display an error because log1(a) is undefined for any a.
  • Negative arguments or bases: The TI-83 will display an error because logarithms are only defined for positive real numbers.
  • Forgetting to press the comma: This will cause the calculator to use the default base of 10 instead of your specified base.
  • Entering the base before the argument: The order matters - the argument comes first, followed by the base after the comma.

FAQ

Can I use the TI-83 to calculate logarithms with any base?
Yes, the TI-83 can calculate logarithms with any positive base (except 1) using the logBASE function.
What happens if I try to calculate log1(a)?
The TI-83 will display an error because log1(a) is mathematically undefined.
How do I clear the last logarithm calculation from the screen?
Press the CLEAR key to remove the current calculation from the display.
Can I use the TI-83 to calculate natural logarithms?
Yes, you can use the 2ND then LN function to calculate natural logarithms (base e).
What if I get an error when entering a logarithm?
Check that you've entered a positive argument and a positive base (not equal to 1). Also ensure you've pressed the comma between the argument and base.