Antilog Table

Introduction

In mathematics, working with large numbers or doing calculations with exponential growth often requires special methods. One useful tool is the antilog table. Antilogarithms are the opposite of logarithms. Logarithms help to reduce large numbers, while antilogarithms bring them back to their original size.

Before electronic calculators were invented, scientists, engineers, and students depended on log and antilog tables to make complex multiplications, divisions, and exponential functions easier. Even today, knowing about antilogs and how to use antilog tables can help people better understand logarithmic ideas that apply in the real world.

 

Table of Contents

• What is an Antilog?
• Why Learn About Antilog Tables?
• How to Use an Antilog Table?
• Using an Antilog Calculator
• Important Antilog Tricks
• Antilog Examples
• Log vs Antilog
• Applications in Real Life
• Practice Questions
• Common Errors
• Tips & Tricks
• Fun Facts
• Conclusion
• FAQs on Antilog Table

 

What is an Antilog?

An antilogarithm (antilog) is the inverse function of a logarithm. If:

log(x) = y, then antilog(y) = x

In base 10, the antilog of a number y is:

antilog(y) = 10^y

For example:

• If log(100) = 2, then antilog(2) = 100

• If log(0.01) = -2, then antilog(-2) = 0.01

Each logarithmic value is made up of:

• Characteristic: The whole number before the decimal.

• Mantissa: The decimal part of the log value.

To find an antilog, you look up the mantissa in the antilog table, then adjust using the characteristic.

 

Why Learn About Antilog Tables?

Understanding antilogs and how to use antilog tables is essential for:

• Solving logarithmic equations manually.

• Understanding concepts in exponential growth, decay, and sound levels.

• Exam preparation where calculators are not allowed.

• Building deeper understanding of number operations in math and science.

 

How to Use an Antilog Table?

Here is a step-by-step guide:

1. Break the number into its characteristic and mantissa.

• For example: 2.347 → Characteristic = 2, Mantissa = 0.347

2. Look up the mantissa in the antilog table.

• Suppose the value at 0.347 is 2.229

3. Multiply the table value by 10^Characteristic

• 2.229 × 10^2 = 222.9

Example:

Find the antilog of 1.45:

• Characteristic = 1

• Mantissa = 0.45

• Antilog of 0.45 = 2.818 (from table)

• Final result: 2.818 × 10^1 = 28.18

 

Using an Antilog Calculator

A quicker method today is using an antilog calculator:

• Just enter the number (e.g., 2.5) and press 10^x

• Output: 10^2.5 = 316.23

This is often available on scientific calculators and mobile apps.

 

Important Antilog Tricks

Here are some helpful tips:

• Learn to separate the characteristic and mantissa.

• For small values, round the mantissa for faster lookup.

• Use known powers of 10:

• Antilog(1) = 10

• Antilog(2) = 100

• Antilog(3) = 1000

 

Antilog Examples

Example 1: Find antilog(3.21)

• Mantissa = 0.21 → Table value = 1.621

• Characteristic = 3 → 10^3 = 1000

• Result = 1.621 × 1000 = 1621

 

Example 2: Antilog of 0.4771

• Close to log(3), so antilog ≈ 3

 

Example 3: Find the antilog of -1.32

• Characteristic = -2 (move one place back)

• Antilog(0.68) ≈ 4.786

• Final result = 4.786 × 10^(-2) = 0.04786

 

Log vs Antilog

 

Applications in Real Life

• Chemistry: pH calculations involve -log[H+]

• Finance: Compound interest formula uses exponents

• Physics: Sound decibels and signal strength

• Biology: Bacterial growth models

• Data Science: Logarithmic regression

 

Practice Questions

1. Find the antilog of 2.56

2. Find the antilog of 0.70

3. Use a calculator to find antilog(4.1)

4. Use the antilog table to evaluate: log(x) = 1.63 → x = ?

5. Convert log(0.0032) to its antilog

 

Common Errors

• Mistaking characteristic as mantissa

• Misreading table values

• Ignoring negative powers

• Forgetting to multiply by 10^Characteristic

 

Tips & Tricks

• Memorise simple antilog values (1, 2, 3)

• Use a rough estimation to check answers

• Practice reading antilog tables accurately

• Avoid using a calculator unless specified

 

Fun Facts

• Logarithms were invented by John Napier in the early 1600s.

• Antilog tables were widely used by NASA scientists before digital computers.

• The term "antilog" is often replaced by exponential functions in higher math.

 

Conclusion

Antilog tables might appear outdated in the era of calculators, but their ideas remain relevant. Knowing how to use an antilog table improves your number sense and analytical thinking. This skill is particularly useful during exams, in science applications, and in areas where logarithmic functions are used regularly. 

By learning to find antilog values either manually or with a calculator, students build confidence in handling exponential data. Engage with problems, experiment with the antilog calculator, and grasp this essential math concept.

 

Related Topics

Sequence and Series - Learn how numbers follow patterns, grow in steps, and build logic through easy explanations of sequences and series.

Sets - Understand how sets group elements, use Venn diagrams, and simplify math problems in a fun and easy way.

Differentiation Questions - Practice solving differentiation questions with step-by-step guidance and strengthen your understanding of calculus concepts.

 

FAQs on Antilog Table

1. How to find antilog with table?

Ans: Break the value into mantissa and characteristic. Use the table to find the mantissa value and multiply it by 10 raised to the characteristic.

 

2. Is antilog always 10?

Ans: No. While base 10 is common, natural logs use base e (2.718). Antilog depends on the base used.

 

3. What is the antilog of any value?
Ans: It is the value of 10 raised to that number. For example, antilog(2) = 100.

 

4. How to find antilog trick?
Ans: Always separate into characteristic and mantissa. Use 10^Characteristic as a multiplier to the table value.

 

5. What is the value of log 1 to 10?

Ans:

For their antilogs, reverse the operation: antilog(log(x)) = x.

 

Learn more about math tables, logarithms, and other essential math concepts at Orchids The International School.