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Last updated on July 5th, 2025

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Antilog Table

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The antilog is the inverse operation of a logarithm. The antilog table is a table used as a reference tool to find the antilog of a number. In this article, we will learn about the antilog table and how to calculate antilog with and without the antilog table.

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What is an Antilog Table

The antilog table is the mathematical tool used to find the antilogarithm of a logarithmic value. The inverse of the logarithmic function is the antilog, that is, if log a = b, then a = antilog b. If log10(a) = b, then a = antilog(b) = 10b.

 

For example, antilog(5) = 105 = 100000
antilog(2.354) = 102.354 = 226

Antilog tables can be categorized into 3 main blocks. The main column is the first block that shows values from .00 to .99, representing the decimal parts.

The second block is the difference column, which has the digits from 0 to 9. The third block is the mean difference column, which has the digits from 1 to 9. 
 

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How to Calculate Antilog?

The antilogarithm is used to reverse the effect of a logarithm and retrieve the original number. The logarithmic value can be divided into two parts: characteristic and mantissa. The integer part is the characteristic, and the decimal part is the mantissa. Thus, the log can be written as: Log (number) = characteristic + mantissa. The characteristic can be positive or negative, but the mantissa should always be positive.

Log of Number 

Characteristic + Mantissa

Characteristic

Mantissa

2.8456

2 + 0.8456

2

0.8456

0.0245

0 + 0.0245

0

0.0245

-4.982

-4 - 0.982 = (-4 - 1) + (1 - 0.982) = -5 + 0.018 

-5

0.018

-0.654

-0 - 0.654 = (-0 -1) + (1 - 0.654) = -1 + 0.346

-1

0.346

 
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What Are the Steps to Find Antilog of a Number?

Let’s learn how to use an antilog table to find the antilog of a number, using the example 2.4681. 

 

Step 1: Identify the characteristic and mantissa
In 2.4681, characteristic = 2 and mantissa = 0.4681

 

Step 2: Using the antilog table to find the base value
The row number can be identified using the first two digits in the mantissa and the column from the third digit, and then from the antilog table, find the corresponding number.   
Here, 0.46 is the row number and 8 is the column number.  

The number is 2936

 

Step 3: Apply the mean difference
Use the fourth digit of the mantissa to find the mean difference from the same row. Add it to the value we get from step 2. 
Here, the fourth digit of the mantissa is 1 
Adding it to 2936: 2936 + 1 = 2937

 

Step 4: Placing the decimal point
Place the decimal point after the number of digits equal to the characteristic + 1.
Here, it is 293.7
The antilog of 2.4681 is 293.7
 

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What is the Antilog of a Number Without Using the Antilog Table?


Let’s find the antilog of a number without the antilog table. We use the formula antilog(x) = 10x, where x is an integer, to find the antilog.

 

Let’s find the antilog(2.345)

Using the formula: antilog(x) = 10x
Antilog of 2.345 = (2.345) = 102.345
Breaking down 102.345: 102.345 = 102 × 100.345

We use a calculator to find the value of 102 and 100.345
102 = 100
100.345 ≈ 2.219

Multiplying the parts: 100 × 2.219 = 221.9 

So, antilog(2.345) = 221.9 
 

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How to Use Antilog Table in Calculations?

Antilog tables are used to simplify the calculations involving multiplication, division, exponents, and roots. Follow these steps to find the antilog:

Step 1: Take the log of the number or expression

Step 2: To expand the logarithmic expression, use the properties of logarithms:
log(xy) = log x + log y
log(x/y) = log x - log y
log xm = m log x

Step 3: Find the logarithm of numbers using the log table and combine the results into a single number

Step 4: Use the antilog table to find the antilog of the logarithmic value we get in step 3.
 

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Common Mistakes and How to Avoid Them in Antilog Table

Students usually make mistakes when working with antilog tables. But it is important for students to learn antilog tables, as it helps them to make calculations easier.

Here are some of the common mistakes and ways to avoid them in the antilog table. 

Mistake 1

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Confusing the log with the antilog table

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Students sometimes use the log table instead of an antilog table, so always check and make sure you are using the antilog table, not the log table. 


 

Mistake 2

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Confusing characteristic and mantissa

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Students sometimes forget to separate the numbers into characteristic and mantissa before using the antilog table, which leads to an error. Always remember that the characteristic is the integer part, and the mantissa is the decimal part of the logarithm of a number. 

Mistake 3

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Errors while placing the decimal point

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Mostly, students tend to find the correct antilog value but make errors when placing the decimal point. So, make sure to place the decimal point in the sum of the mean difference and the antilog. 

Mistake 4

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Misreading the wrong row or column in the antilog table

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Misreading the digits in the antilog table is common among students, and it results in an error. So always double-check whether the value is correct or not, and also use a ruler to find the value. 

Mistake 5

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Forgetting to multiply by 10^characteristic 

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Not multiplying the antilog of the mantissa by the 10^characteristic is one of the mistakes that students often repeat. To avoid this error, students should always multiply the antilog of the mantissa by the 10characteristic. For example, if the characteristic is 2 and the antilog of the mantissa is 2.942, then the antilog is calculated by multiplying 2.942 by 102. So, 2.942 × 100 = 294.2

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Real-world Applications of Antilog Table

The antilog table is a tool we use in science, engineering, and finance to find the number when it is given in logarithmic form. Here are some of the real-life applications of the antilog table. 

 

  • To perform scientific calculations in chemistry, physics, and biology involving logarithms, we use an antilog table. 

 

  • Antilog tables are used to solve problems involving exponential growth and decay.

 

  • Antilogarithms are used to convert logarithmic values back to actual quantities. For example, to find the energy released from an earthquake and to calculate the star’s brightness from its logarithmic magnitude. 
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Solved Examples of Antilog Table

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Problem 1

Find the antilog of 2.3010

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The antilog of 2.3010 is 200

Explanation

 Identifying the characteristic and mantissa of 2.3010
Here, characteristic = 2
Mantissa = 0.3010
The value corresponding to the 30th row and 1st column is the antilog(0.3010). 
The corresponding value is 2.000, after adding the decimal point.
Here, the mean difference is 0, so 2.000 + 0 = 2.000
x = 2.000 × 102 = 200

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Problem 2

Find the antilog of 0.8451

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Antilog(0.8451) = 7

Explanation

Using the equation antilog(x) = 10x
Since, antilog(0.8451) = 100.8451
The value of 100.845 = 6.998 ≈ 7 
The antilog is approximately 7.
 

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Problem 3

Find the antilog of 1.2553

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The value of antilog 1.2553 = 18

Explanation

To find the antilog of 1.2553, we first identify the characteristic and mantissa
Here, the characteristic = 1
Mantissa = 0.2553
Check the value corresponding to the 25th row and 5th column, to find the antilog value
From the antilog table, the value is 1799
Adding the mean difference, which is 1 to 1799:
 1799 + 1 = 1800
Now we add the decimal point: 1.800
Multiplying the number by 10^characteristic
Here, the characteristic is 1
Therefore, 1.800 × 101 = 18.00
 

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Problem 4

Find the antilog of 4.0792

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The antilog of 4.0792 is 12000

Explanation

Using the equation, antilog(x) = 10x
So, antilog(4.0792) = 104.0792
Breaking 104.0792 as 104 × 100.0792
104 = 10000
100.0792 = 1.2000
Multiplying the parts: 10000 × 1.2000 = 12000
 

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Problem 5

Find the antilog of 2.8451

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Antilog(2.8451) = 700

Explanation

Identifying the characteristic and mantissa, to find the antilog of 2.8451
Here, characteristic = 2
Mantissa = 0.8451
The value corresponding to the 84th row and the 5th column, to find the antilog value
So, here the value is 6998
Here, the mean difference is 1
Adding the mean difference: 6998 + 1 = 6999
Adding decimal points equal to 2.8451 in 6999: 6.999 
Multiplying by 102 as 2 is the characteristic 
6.999 × 102 = 699.9
≈ 700
 

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FAQs on Antilog Table

1.What is an antilog table?

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2.What are the parts of a logarithm?

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3.What is antilog?

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4.What is the use of an antilog table?

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5.What is the value of the antilog of 3?

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6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?

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7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Antilog Table?

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8.How do technology and digital tools in Saudi Arabia support learning Algebra and Antilog Table?

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9.Does learning Algebra support future career opportunities for students in Saudi Arabia?

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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