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How to Put Log Base in Ti-84 Calculator

Reviewed by Calculator Editorial Team

Calculating logarithms with custom bases on your TI-84 calculator is straightforward once you understand the change of base formula. This guide will walk you through the process step-by-step, including how to use the built-in logarithm functions and perform manual calculations when needed.

Introduction

The TI-84 calculator is a powerful tool for students and professionals alike, offering a wide range of mathematical functions. One common need is to calculate logarithms with bases other than the natural logarithm (base e) or common logarithm (base 10).

Logarithms with custom bases can be calculated using the change of base formula, which allows you to convert any logarithm to a form that your calculator can handle. This guide will show you how to do this efficiently on your TI-84.

Using the Calculator

Your TI-84 has built-in functions for natural logarithms (ln) and common logarithms (log). To calculate logarithms with other bases, you'll use the change of base formula:

Change of Base Formula:

logb(x) = ln(x) / ln(b)

or

logb(x) = log(x) / log(b)

Step-by-Step Instructions

  1. Press the 2ND key and then the LN key to access the natural logarithm function.
  2. Enter the number you want to find the logarithm of (x).
  3. Press the / key.
  4. Press the 2ND key and then the LN key again.
  5. Enter the base (b) of the logarithm.
  6. Press the = key to get the result.

For example, to calculate log2(8):

  1. Press 2ND then LN.
  2. Enter 8.
  3. Press /.
  4. Press 2ND then LN.
  5. Enter 2.
  6. Press = to get 3.

Tip: You can also use the common logarithm (log) function by pressing 2ND then LOG instead of LN. This method is useful when working with base 10 logarithms.

Manual Calculation

If you prefer to understand the underlying mathematics or need to verify your calculator's results, you can perform the calculation manually using the change of base formula.

Example Calculation

Let's calculate log3(27):

  1. Identify the base (b = 3) and the number (x = 27).
  2. Use the change of base formula: log3(27) = ln(27) / ln(3).
  3. Calculate ln(27) ≈ 3.2958.
  4. Calculate ln(3) ≈ 1.0986.
  5. Divide the results: 3.2958 / 1.0986 ≈ 3.

The result is 3, which makes sense because 33 = 27.

Note: For more precise calculations, you can use the calculator's built-in natural logarithm function to get more decimal places.

Common Logarithm Bases

While you can calculate logarithms for any base, some bases are used more frequently than others. Here are a few common examples:

  • Base 2: Used in computer science and information theory.
  • Base 10: Common in mathematics and engineering.
  • Base e (≈2.71828): Used in natural logarithm calculations.
  • Base 16: Used in hexadecimal number systems.

For these common bases, you can use the calculator's built-in functions or the change of base formula as needed.

FAQ

Can I calculate logarithms with any base on my TI-84?
Yes, you can calculate logarithms with any base using the change of base formula. Your TI-84 has built-in functions for natural and common logarithms, which you can use to derive logarithms for other bases.
What is the difference between natural and common logarithms?
Natural logarithms use base e (approximately 2.71828), while common logarithms use base 10. The TI-84 has separate keys for these functions: LN for natural logarithms and LOG for common logarithms.
How do I clear the last entry on my TI-84?
To clear the last entry, press the 2ND key and then the DEL key. This will remove the most recent input or calculation.
Can I use the TI-84 for scientific calculations?
Yes, the TI-84 is capable of performing a wide range of scientific calculations, including logarithms, exponentials, trigonometric functions, and more. It's a versatile tool for students and professionals.