How to Put Log 1 2 in Calculator Ti-83

Calculating logarithms on your TI-83 calculator is straightforward once you know the correct sequence of steps. This guide will walk you through entering log base 2 of 1 (log₂1) on your TI-83 calculator, explain the mathematical concept, and provide practical examples.

How to Calculate log 1 2 on TI-83

The TI-83 calculator can compute logarithms with any base, not just natural logarithms (ln) or common logarithms (log). To calculate log base 2 of 1 (log₂1), you'll need to use the change of base formula.

Key Information

The result of log₂1 is 0 because any number raised to the power of 0 equals 1 (2⁰ = 1). This is a fundamental logarithmic identity.

Basic Steps

Press the 2ND key and then the LOG key to access the log function.
Enter the number 1 (the argument of the logarithm).
Press the 2ND key again, then the , key to enter a comma.
Enter the base 2.
Press the = key to calculate the result.

Your calculator should display 0 as the result, confirming that log₂1 = 0.

Step-by-Step Guide

Let's break down the process in more detail:

Step 1: Access the Log Function

Press the 2ND key, then the LOG key. This accesses the logarithm function. The calculator will display "log(" on the screen.

Step 2: Enter the Argument

Enter the number 1. The screen will now show "log(1".

Step 3: Enter the Comma

Press the 2ND key again, then the , key. This enters a comma in the function. The screen will now show "log(1,".

Step 4: Enter the Base

Enter the number 2. The screen will now show "log(1,2".

Step 5: Calculate the Result

Press the = key. The calculator will display 0, which is the result of log₂1.

Pro Tip

Remember that the base must always be entered after the comma. Entering the base before the comma will result in an error.

The Formula Explained

The logarithm function logₐb (log base a of b) asks the question: "To what power must a be raised to obtain b?"

Logarithm Formula

logₐb = x means aˣ = b

For log₂1, we're asking: "To what power must 2 be raised to obtain 1?" The answer is 0, because 2⁰ = 1.

Change of Base Formula

If your calculator only has natural logarithm (ln) and common logarithm (log) functions, you can use the change of base formula:

Change of Base Formula

logₐb = ln(b)/ln(a)

For log₂1, this would be ln(1)/ln(2). Since ln(1) = 0, the result is 0.

Worked Examples

Example 1: log₂1

Using the steps above:

Press 2ND LOG → "log(" appears
Enter 1 → "log(1" appears
Press 2ND , → "log(1," appears
Enter 2 → "log(1,2" appears
Press = → 0 appears

Example 2: log₂2

Following the same steps:

Press 2ND LOG → "log(" appears
Enter 2 → "log(2" appears
Press 2ND , → "log(2," appears
Enter 2 → "log(2,2" appears
Press = → 1 appears

This makes sense because 2¹ = 2.

Logarithm Examples
Expression	Result	Explanation
log₂1	0	2⁰ = 1
log₂2	1	2¹ = 2
log₂4	2	2² = 4
log₂8	3	2³ = 8

Frequently Asked Questions

What does log 1 2 mean?

log 1 2 means log base 2 of 1, which asks "To what power must 2 be raised to obtain 1?" The answer is 0 because 2⁰ = 1.

Why is log 1 2 equal to 0?

log 1 2 equals 0 because any number raised to the power of 0 equals 1. Specifically, 2⁰ = 1, so log₂1 = 0.

Can I calculate logarithms with other bases on TI-83?

Yes, the TI-83 can calculate logarithms with any base using the change of base formula. You enter the argument first, then the base after a comma.

What happens if I enter the base before the argument?

If you enter the base before the argument, the TI-83 will display an error because the logarithm function requires the argument first, then the base.

Is log 1 2 the same as ln 1?

No, log 1 2 (log base 2 of 1) is not the same as ln 1 (natural logarithm of 1). While both equal 0, they represent different logarithmic scales.