How To Get Log Base On Ti 84

How to Calculate Logarithms with Any Base on the TI‑84 Calculator

When you’re working on algebra, calculus, or data analysis, logarithms pop up all the time. The TI‑84 series of graphing calculators, a staple in many high‑school and college classrooms, makes this easy—provided you know how to use its built‑in functions. While the calculator offers direct access to natural logarithms (ln) and common logarithms (log base 10), you’ll often need a logarithm with an arbitrary base. This guide walks you through the process step by step, explains the underlying math, and gives you tips for quick calculations and troubleshooting.

Introduction

The TI‑84 can compute logarithms of any base using the change‑of‑base formula:

[ \log_b a = \frac{\log_c a}{\log_c b} ]

where c is any base that the calculator can handle (normally 10 or e). In practice, the calculator’s log button represents base 10, and ln represents base e (the natural logarithm). By combining these two functions, you can derive logarithms for any base b you desire.

Step‑by‑Step Procedure

1. Identify the Desired Logarithm

Suppose you need (\log_2 32). Here, a = 32 and b = 2.

2. Open the Calculator and Clear the Screen

Press ON, then CLEAR to start fresh Turns out it matters..

3. Input the Numerator

• Press log (base 10) or ln (base e) depending on your preference.
  Tip: Using log is often quicker because the TI‑84’s log key is directly on the screen Worth keeping that in mind..

• Enter the value a (32 in our example).
  The display should read log(32) Most people skip this — try not to..

4. Divide by the Denominator’s Logarithm

• Press the division key ÷.
• Now enter the logarithm of the base b:
  • Press log or ln again.
  • Input the base value (2).
  • The expression becomes log(32) ÷ log(2).

5. Execute the Calculation

Press ENTER. The TI‑84 will display the result, which should be 5 for (\log_2 32).

Using the Change‑of‑Base Formula on TI‑84

Because the TI‑84 lacks a dedicated “log base b” button, we rely on the change‑of‑base identity:

[ \log_b a = \frac{\log a}{\log b} ]

The calculator can compute log(a) and log(b) in base 10 or ln(a) and ln(b) in base e. Both routes yield the same result because the ratio of the two logarithms is independent of the chosen common base And it works..

Example: (\log_7 49)

1. Type log(49) → log(49).
2. Press ÷, then log(7).
3. ENTER → Result: 2.

If you prefer natural logs:

1. ln(49) → ln(49).
2. ÷, then ln(7).
3. ENTER → Result: 2.

Practical Tips for Speed and Accuracy

Common Mistakes and How to Avoid Them

1. Forgetting the division
   Problem: Typing log(32) log(2) without the division operator.
   Fix: Always include ÷ between the two logs.

2. Using the wrong base for both logs
   Problem: Mixing log and ln inconsistently.
   Fix: Stick to one base for both logs; the result will be the same, but consistency reduces confusion.

3. Entering the base as a fraction
   Problem: Trying to input log(32) ÷ log(1/2) directly.
   Fix: Input the base as a decimal or a fraction using the ALPHA key: ALPHA → 1 → 2 → ÷ → 1 → ALPHA → 1 → 2 → ÷. The calculator will interpret it correctly Turns out it matters..

4. Neglecting parentheses
   Problem: log 32 ÷ log 2 may be misread by the calculator.
   Fix: Use parentheses to group each logarithm: log(32) ÷ log(2) Nothing fancy..

FAQ

Q1: Can I use the TI‑84 to compute (\log_{-2} 8)?

A: No. Logarithms are defined only for positive bases and positive arguments. The calculator will display an error.

Q2: Is there a faster way to compute (\log_2 64) than using the change‑of‑base formula?

A: Yes. Recognize that (64 = 2^6), so (\log_2 64 = 6). But if you’re unfamiliar with the exponent, the change‑of‑base method is reliable.

Q3: Does the TI‑84 Plus CE allow a direct “log base” function?

A: The TI‑84 Plus CE (and newer models) includes a log function that accepts two arguments: log(b, a). This directly returns (\log_b a). If you have this model, simply type log(2,32) for (\log_2 32) That's the part that actually makes a difference..

Q4: How do I store a frequently used base like 3 for future calculations?

A: Press STO> after typing 3, then RCL whenever you need it. For example:

• 3 STO> saves 3 in register 1.
• Later, log(27) ÷ log(RCL) will use the stored base.

Q5: Why does the result sometimes show more decimal places than I need?

A: The TI‑84 defaults to 4 decimal places. To change this, go to 2nd → MODE and set the desired number of decimal places.

Scientific Explanation

Logarithms satisfy the property:

[ \log_b a = \frac{\log_c a}{\log_c b} ]

This comes from the definition of logarithms as the inverse of exponentiation. If (b^x = a), taking the logarithm of both sides with base c gives:

[ x = \frac{\log_c a}{\log_c b} ]

The TI‑84 can compute (\log_c a) for c = 10 or c = e (natural log). By dividing one by the other, we isolate x, which is exactly (\log_b a).

Conclusion

Calculating logarithms with arbitrary bases on a TI‑84 is straightforward once you understand the change‑of‑base principle. Remember to keep your expressions clear, use parentheses, and store frequently used values to streamline your workflow. Now, by entering the numerator and denominator logs, dividing them, and executing the calculation, you’ll obtain accurate results in seconds. Whether you’re tackling algebraic equations, solving exponential growth problems, or simply satisfying curiosity, mastering this technique will make the TI‑84 an even more powerful tool in your mathematical arsenal.