How to Calculate Antilogarithms Using an Antilog Table with Examples

Antilog Table: Before calculators and computers, people used antilog tables to solve problems involving logarithms and exponents. These tables made it easier to calculate large or small numbers without doing complex math by hand.

What is an Antilog?

Ever heard of a log? No, not the wooden one! In math, a logarithm is a special way to write big numbers. So, what is antilog? An antilog is just the reverse! It helps you go back to the big number from its log form.

What is antilog used for?

• To undo the effect of a logarithm.

• To find the actual number when we already know its log.

Antilog Example:

What is an Antilog Table?

Here's how the antilog table works

1. Logarithms simplify multiplication and division by transforming them into addition and subtraction.
2. An antilog table reverses this process by providing the number associated with a given logarithmic value.

For example:

Why Use an Antilog Table? 

The antilog table helps us find the real number from a logarithmic value. It saves time and effort, especially when calculators aren't around.

You use the antilog table when you need to:

• Calculate the antilog of a number.

• Solve tricky math or science problems.

• Understand how things were calculated before computers.

Enroll Now for Kids Online Classes

How to Calculate Antilog Using Antilog Formula  ?

For example:

• If log (500) = 2.698 , the mantissa is 0.698.
• If log⁡ (1000) = 3.0, the mantissa is 0 .
• If log (0.01) = −2.0, the mantissa is 0 .

Example 1: log (500) = 2.698. The characteristic is 2 because there are 3 digits to the left of the decimal in 500, and 3 − 1 = 2.

Example 2 : log⁡ (1000) = 3.0. The characteristic is 3 because there are 4 digits to the left of the decimal in 1000, and 4 − 1 = 3.

For numbers less than 1, the characteristic is calculated by counting the zeros immediately following the decimal point, negating this count, and subtracting one.

Example 1 : log⁡ (0.01) = −2.0. The characteristic is −2 because there is 1 zero after the decimal in 0.01, and −(1 + 1) = −2.

Example 2: log⁡ (0.001) = −3.0. The characteristic is −3 because there are 2 zeros after the decimal in 0.001, and −(2 + 1) = −3

x= 10 ^log⁡(x) = 10 ^{Characteristic+Mantissa}

Example 1: Find antilog (2.4567 )

Step 1: Break the logarithmic value into the characteristic and mantissa

• Given log⁡ (x) = 2.4567
• Characteristic = 2 (the integer part).
• Mantissa = 0.4567 (the fractional part).

Step 2: Use the antilogarithm formula

Step 3: Calculate each term

• 10 ² =  100
• 10 ^0.4567 =  2.8622

Step 4: Multiply the results

Example 2: Find antilog (4.5234)

Recall the antilog formula :

Given logarithmic value :

Break x into the characteristic and mantissa :

Characteristic = 4 (integer part).

Mantissa = 0.5234 (decimal part).

Calculate 10 ⁴ :

Calculate 10 ^0.5234

Multiply the results :

Steps to Calculate Antilog Using an Antilog Table

Example 1: Calculate the antilog of 2.6452

Solution:

Step 1: Separate the characteristic and mantissa

• Characteristic = 2 (integer part).
• Mantissa = 0.6452 (decimal part).

Step 2: Use the antilog table for the mantissa

1. Look for the row 0.64 , which represents the first two decimal places of the mantissa.
2. Then locate column 5, which corresponds to the third digit of the mantissa ( 0.645 ).
3. The value found at row 0.640, column 5, is 4416.

Step 3: Use the mean difference for the fourth digit

• The fourth digit of the mantissa is 2 .
• Using the mean difference columns in the same row, 0.64 , find the value for column 2 .
• The value corresponding to this is 2.

Step 4: Add the values from steps 2 and 3

Step 5: Insert the decimal point

• To determine the decimal point's position, add 1 to the characteristic ( 2 + 1 = 3 ).
• This means the decimal point will be placed after the third digit from the left in 4418

Result: 4418 → 441.8

Example 2: Calculate the antilog of 2.7845

Given logarithm: 2.7845

Characteristic : 2

Mantissa : 0.7845

Find the value for the first three digits of the mantissa ( 0.784 ):

Adjust for the fourth digit ( 5 ) using the mean difference:

Add the base value and the mean difference:

Insert the decimal point:

Understanding the Anti Log Formula 

The anti log formula is easy to remember:

antilog(x) = 10^x

It means raise 10 to the power of the log value.

Antilog Example:

antilog(3.2) = 10^3.2 = around 1584.9

This formula helps students calculate antilog quickly and correctly.

Difference Between Antilogarithm and Logarithm Tables

Real-Life Use of Antilog Tables 

Antilog tables are still useful in science experiments and when power goes out and no calculators are around! Even today, many teachers love to show antilog examples to help kids understand numbers better.

Knowing how to find antilog gives you superpowers in math and science classes.

Where Do We Use Antilogs Today? 

Did you know that computers, scientists, and even astronauts use antilogs to solve equations? When working with sound, light, earthquakes, and chemistry, knowing how to find antilog helps a lot.