How to Use an Antilog Table: Step-by-Step Guide with Examples
The concept of Antilog Table plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. If you've ever solved calculations involving logarithms in board exams or competitive tests like JEE, you've probably used antilog tables to find the original number from its logarithm—making calculations faster and more accurate.
What Is Antilog Table?
An Antilog Table is a mathematical chart that helps you quickly find the antilogarithm (the number whose logarithm is a given value), especially when calculators are not allowed. For any given logarithm value (usually base 10), the table provides the original number. This is super helpful in solving problems related to logarithmic functions, exponential calculations, and scientific computations.
Key Formula for Antilog Table
Here’s the standard formula: \( \text{Antilog}(x) = 10^x \)
If \( \log_{10} y = x \), then \( y = \text{Antilog}(x) = 10^x \).
Why Use Antilog Tables?
Antilog tables are mostly used in exams where electronic calculators are not allowed. They make multiplication, division, root and power calculations much quicker. You’ll often use them in NCERT Class 11 and 12 maths, chemistry, physics, engineering, and competitive exams. Having this skill helps boost speed and accuracy in the main maths paper!
Parts of a Logarithm: Characteristic & Mantissa
When you have a logarithm such as 2.4783, it is separated into:
- Characteristc: The whole number part (here, “2”)
- Mantissa: The decimal part (here, “0.4783”)
When using the antilog table, you always look up the mantissa. The characteristic tells you where to place the decimal in the final answer.
Step-by-Step Illustration: How to Use the Antilog Table
- Separate the number into characteristic and mantissa.
Example: For 2.5463, characteristic = 2, mantissa = 0.5463 - Find the row for the first two digits after the decimal (here: 54), and the column for the third digit (here: 6) in the Antilog Table.
Look up the value at row “.54” and column “6” - Add the mean difference (the fourth digit, 3) to the value found.
If mean difference for 3 is “2”, add this: Table value + 2 - Place the decimal. Count characteristic + 1 digits from the left.
Answer will be in the form: 3518 ⇒ 3.518 × 10^2 = 351.8
Sample Antilog Table (Excerpt)
| Mantissa | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| .54 | 3512 | 3513 | 3514 | 3515 | 3516 | 3516 | 3517 | 3518 | 3519 | 3520 |
For a full printable table, download the Antilog Table PDF.
Example Calculation Using Antilog Table
Let’s solve:
Find the antilog of 2.7531
1. Identify characteristic (2) and mantissa (0.7531)
2. In the table, find row “.75” and column “3” — value is 5662
3. Add the mean difference for “1” (let’s say it’s 2): 5662 + 2 = 5664
4. Decimal goes after 3 digits (characteristic + 1): 566.4
Final Answer: Antilog(2.7531) = 566.4
Speed Trick: Using The Calculator
Don’t have a table handy? Use the formula Antilog(x) = 10x. For 2.7531:
1. Enter 2.7531
2. Calculate 10^2.7531 (use the calculator’s exponent function)
3. You’ll get approximately 566.4 — same as above!
Cross-Disciplinary Usage
The Antilog Table is useful in Maths, Physics (pH calculations, decibel levels), Chemistry (concentration calculations), Statistics, and even Computer Science (logarithmic complexity). In exponential equations, they help revert log-transformed data back to its original scale.
Frequent Errors and Misunderstandings
- Not separating characteristic and mantissa before looking up the value.
- Adding the mean difference to the wrong cell in the table.
- Incorrect placement of the decimal point (remember: it’s characteristic + 1 digits!).
- Using the wrong base (antilog tables are usually base 10).
Antilog Table vs Calculator
| Feature | Antilog Table | Calculator |
|---|---|---|
| Allowed in all exams? | Yes (mostly) | No (many boards restrict use) |
| Speed | Fast (with practice) | Very fast |
| Accuracy | Up to 4 decimal places | Up to 9+ decimal places |
| Learning Value | High (conceptual understanding) | Limited (just press buttons) |
Try These Yourself
- Find the antilog of 1.2684 using the table.
- Explain how to use the mean difference column for five-digit logs.
- Use your Antilog Table to find the value of −2.4071.
- Compare answers using the table and a scientific calculator for 3.0196.
Relation to Other Concepts
The Antilog Table links directly with log tables, exponents & powers, and logarithmic equations. Mastering the antilog process makes it easier to handle questions in competitive exams—especially those involving root or exponential form.
Classroom Tip
A quick way to remember: Separate—Find—Add—Decimal. Vedantu’s teachers break down every Antilog Table exercise so you can master log-to-antilog conversions smoothly, even under time pressure. Practicing solved examples and verifying with a calculator boosts your exam confidence.
We explored Antilog Table—from definition, formula, step-by-step table use, solved examples, and common mistakes, to calculator comparison. Go ahead and solve more! For detailed logs, exponents, and related practice, check these useful pages:
FAQs on Antilog Table in Maths – Definition, Steps & Examples
1. What is an antilog table in Maths?
An antilog table is a mathematical tool used to find the antilogarithm (or original number) given its logarithm value. It's essentially the reverse process of finding a logarithm. If logb y = x, then y = antilogb x. Antilog tables are commonly used with base 10 logarithms.
2. How do I use an antilog table to solve logarithmic problems?
Using an antilog table involves these steps:
• **Separate the characteristic and mantissa:** The logarithm is expressed as characteristic + mantissa (e.g., 2.5463; characteristic = 2, mantissa = 0.5463).
• **Locate the mantissa in the table:** Find the row corresponding to the first two digits of the mantissa and the column corresponding to the third digit. Note the value at the intersection.
• **Add the mean difference:** Find the mean difference for the fourth digit in the same row. Add this value to the previously found value.
• **Place the decimal:** The number of digits before the decimal point is (characteristic + 1).
• **This gives you the antilog.
3. Can I download an antilog table PDF?
Yes, many websites offer antilog table PDFs for download. Search online for "antilog table PDF" to find various resources. Some may be specifically for Class 11 or 12, or for competitive exam preparation.
4. What happens if the logarithm is negative? How to find the antilog?
If the logarithm is negative, you must first adjust it into characteristic and mantissa form before using the antilog table. Add and subtract 1 to make the mantissa positive. For example, -8.053 becomes -9 + 0.947. The characteristic is -9, and the mantissa is 0.947. After finding the antilog of the mantissa using the table, multiply the result by 10 raised to the power of the characteristic.
5. Is antilog always the reverse operation of log?
Yes, the antilog is the inverse operation of the logarithm. If logb y = x, then antilogb x = y. They are inverse functions of each other.
6. Why is the mantissa used in an antilog table instead of the integer part?
The mantissa represents the fractional part of the logarithm. The antilog table is designed to provide the numerical value associated with this fractional part, independent of the integer part (characteristic), allowing for a concise table lookup.
7. How do examiners mark calculation steps if tables are used rather than calculators?
Examiners usually provide partial credit for correctly applying log and antilog table procedures. Showing each step, including the characteristic and mantissa separation, table lookup values, and final result, is crucial for maximum marks. It demonstrates understanding of the method.
8. What are the typical errors students make while using antilog tables in speed tests?
Common errors include:
• Incorrectly separating the characteristic and mantissa
• Misreading values from the antilog table
• Errors in adding the mean difference
• Incorrect placement of the decimal point
Practicing regularly with a focus on accuracy and speed can help minimize these mistakes.
9. Are antilog tables allowed in all competitive or board exams?
The permissibility of antilog tables varies depending on the specific exam. Always check the exam's rules and regulations beforehand. Some exams may allow them, while others may require the use of calculators.
10. How do antilog tables compare with scientific calculators in accuracy and speed?
Scientific calculators generally provide greater accuracy and speed than antilog tables. However, understanding antilog tables helps build a foundational understanding of logarithms and can be useful when calculators aren't permitted.
11. How can I improve my speed in solving log-antilog problems?
Practice regularly using both antilog tables and calculators. Focus on mastering the steps of using the table accurately and efficiently. Memorize common log and antilog values for faster calculation.
12. What are the applications of antilog tables beyond classroom calculations?
Antilog tables, while less frequently used with modern calculators, have applications in various fields where logarithmic scales are employed such as decibel calculations in acoustics, pH calculations in chemistry, and certain engineering applications.
