How to Put Log Base in Calculator Ti 83

Introduction

The TI-83 calculator is a powerful tool for performing mathematical calculations, including logarithmic functions. While the calculator has a built-in natural logarithm function (ln), it doesn't directly support logarithms with custom bases. However, you can calculate logarithms with any base using the change of base formula.

This guide will walk you through the process of using this formula to calculate logarithms with custom bases on your TI-83 calculator.

Basic Logarithm Function

The TI-83 calculator has a built-in natural logarithm function, which is represented by the "ln" key. To use this function, follow these steps:

1. Press the "2ND" key.
2. Press the "LN" key to access the natural logarithm function.
3. Enter the number for which you want to calculate the logarithm.
4. Press the ")" key to close the parentheses.
5. Press the "ENTER" key to get the result.

For example, to calculate ln(10), you would press: 2ND LN 10 ) ENTER.

Setting a Custom Base

To calculate a logarithm with a custom base, you'll need to use the change of base formula. Here's how to do it on your TI-83 calculator:

1. Press the "2ND" key.
2. Press the "LN" key to access the natural logarithm function.
3. Enter the number for which you want to calculate the logarithm.
4. Press the ")" key to close the parentheses.
5. Press the "/" key to divide.
6. Press the "2ND" key.
7. Press the "LN" key again.
8. Enter the base of the logarithm.
9. Press the ")" key to close the parentheses.
10. Press the "ENTER" key to get the result.

For example, to calculate log₂(8), you would press: 2ND LN 8 ) / 2ND LN 2 ) ENTER.

Examples

Let's look at a few examples to illustrate how to use the change of base formula on your TI-83 calculator.

Example 1: log₁₀(100)

To calculate log₁₀(100), follow these steps:

1. 2ND LN 100 ) / 2ND LN 10 ) ENTER

The result should be 2, since 10² = 100.

Example 2: log₂(16)

To calculate log₂(16), follow these steps:

1. 2ND LN 16 ) / 2ND LN 2 ) ENTER

The result should be 4, since 2⁴ = 16.

Example 3: log₅(125)

To calculate log₅(125), follow these steps:

1. 2ND LN 125 ) / 2ND LN 5 ) ENTER

The result should be 3, since 5³ = 125.

Troubleshooting

If you're having trouble calculating logarithms with custom bases on your TI-83 calculator, here are some common issues and solutions:

Issue: Calculator displays "ERROR"

This error can occur if you enter an invalid base or argument. Make sure that:

• The base is a positive real number greater than 1 and not equal to 1.
• The argument is a positive real number.

Issue: Result is not as expected

Double-check your calculations and ensure that you're using the correct base and argument. You can also try calculating the same logarithm using a different method to verify the result.

Issue: Calculator is slow or unresponsive

If your calculator is running slowly, try clearing the memory and restarting it. You can also try using a different battery to ensure that the issue is not related to the power source.