Antilog Table

Antilog Table is a mathematical and technical reference tool for determining the values of Antilogarithms, which are the inverse operations of logarithms. Antilog returns pre-calculated exponential values corresponding to particular logarithmic inputs. Before calculators and computers, these tables were commonly used to simplify difficult computations requiring exponentiation and logarithmic transformations.

Antilog tables allowed for the rapid retrieval of values without the need for real arithmetic calculations. Digital technologies have largely supplanted the need for physical Antilog tables in modern times, making computations more efficient and exact. In this article, we will learn about the Antilog table in detail including its use to find the value of antilog.

What is an Antilog?

Antilog is the inverse operation of the logarithm. Antilog is used to find the result for which the base has been raised to a certain power. Basically, the output for the log is input for antilog and vice-versa. Antilog is basically used for calculation in digital technologies.

What is Antilog Table?

Antilog Table is a mathematical reference tool used to calculate the values of Antilogarithms, which are logarithmic inverse operations. By transforming multiplication and division into addition and subtraction, logarithms are used to simplify difficult computations involving big numbers or exponential development. An Antilog table allows you to quickly identify the original numbers that correspond to specified logarithmic values.

Antilog generally provides values for a variety of logarithmic bases as well as their Antilogarithmic values. This table was extremely useful before the introduction of calculators and computers since it aided in manual computations and data processing. However, as digital technology and scientific calculators have advanced, the use of Antilog tables has reduced.

Antilog Formula

As we already discussed, the antilog is the method of getting the value of an exponentiated number, which is the inverse operation of taking the logarithm of a number. The formula for antilog is given as follows:

antilog(x) = 10^x

How to Calculate Antilog?

As the logarithm of any number can be divided into two parts: the characteristic and the mantissa. These components help us calculate the value of the antilogarithm for any given logarithmic value.

To calculate the antilogarithm (also known as the inverse logarithm) using the characteristic and mantissa, you need to understand the structure of a logarithmic number. A logarithm can be represented as:

Log(x) = Characteristic + Mantissa

Here, 

• Log(x) is the logarithm of the number you want to find the antilogarithm for,
• Characteristic is the integer part of the logarithm, and
• Mantissa is the fractional part of the logarithm.

To find the antilogarithm, we need to calculate, x = 10^Log(x) [As log is the inverse operation of antilog].

Let’s consider an example to understand it better.

Example: Find antilog(2.4567).

Solution:

Let’s us assume Log(x) = 2.4567, [Where x is the antilog of 2.4567]

Here, Characteristic = 2 (integer part)
Mantissa = 0.4567 (fractional part)

x = 10² × 10^0.4567 [10^0.4567 ≈ 3.016]

x = 100 × 3.016

x = 301.6

So, the antilog(2.4567) is approximately 301.6.

Common Antilog Table

Here is the common table of antilog which also refer to as antilog table 1 to 100.

How to Find Antilog of a Number using Antilog Table?

Calculating the Antilog using an Antilog table involves breaking down the given logarithm into its characteristic and mantissa parts. Let’s walk through the steps to calculate the Antilog of the number 1.4317 using an Antilog table:

Step 1: Given logarithm: 1.4317.

Separate the integral part (characteristic) from the fractional part (mantissa):

• Characteristic: 1
• Mantissa: 0.4317

Step 2: Find the equivalent value of mantissa using the antilog table. Find the row number that equals .43 and then select column number 1 is the matching value.

Step 3: Proceed to the mean difference column. Use the .56 row again and get the appropriate value in column 8. The value in this case is 7.

Step 4: Add the values you discovered in steps 2 and 3. It is 2698 + 7 = 3697 in this case.

Step 5: Insert the decimal point now. The decimal point always goes in the correct position. You must multiply the characteristic value by 1. You now have 3. Then, after 3 digits, add the decimal point to obtain 369.7.

As a result, the antilog value of 2.5678 is 369.7.

Calculate Antilog using Calculator

Using a calculator to calculate the Antilogarithm is a simple technique. Most scientific calculators contain a specific button for calculating Antilogarithms, which is typically labelled “10^x” or “antilog.” Thus, you can use following steps to find antilog with any scientific calculator.

• Step 1: Use a scientific calculator with an “antilog” or “10^x” button.
• Step 2: Input the given logarithm.
• Step 3: Calculate the antilog using the “10^x” button on the calculator.

Antilog from 1 to 10

The following table represents the value of antilog from 1 to 10.

Antilog of n	Expression	Result
Antolog of 1	antilog(1)	10
Antolog of 2	antilog(2)	100
Antolog of 3	antilog(3)	1,000
Antolog of 4	antilog(4)	10,000
Antolog of 5	antilog(5)	100,000
Antolog of 6	antilog(6)	1,000,000
Antolog of 7	antilog(7)	10,000,000
Antolog of 8	antilog(8)	100,000,000
Antolog of 9	antilog(9)	1,000,000,000
Antolog of 10	antilog(10)	10,000,000,000

Antilog and Log Table

Antilog and Log Tables are both valuable reference tables in mathematics, as well as in physics and chemistry. They are used to manually calculate complex calculations involving exponentials and logarithms. However, there are some key differences between both tables, and these differences are listed as follows:

Aspect	Antilog Table	Log Table
Purpose	Helps find the original (anti-log) value from its logarithm.	Helps in finding the logarithm of a given value.
Content	Contains values representing the exponential of the logarithm.	Contains logarithmic values, typically base 10 or base e (natural logarithm).
Usage	Used to perform exponentiation or find the result of exponentiation.	Used to perform logarithmic operations or find the result of such operations.
Example	If you have log base 10 of 2 (log10(2)), you can find the antilog, which is 102 = 100.	If you have a numerical value like 100, you can find its logarithm, which is log base 10 of 100 i.e., log10(100) = 2.
Application	Commonly used in calculations involving exponential growth or decay.	Commonly used in mathematics, engineering, and science for various calculations involving orders of magnitude, exponentiation, and more.

Antilog Table PDF

The team at GeeksforGeeks created this antilog table PDF to help students in their mathematical calculations and logarithmic operations. This comprehensive resource provides a valuable reference for quickly finding antilogarithm values, making it an essential tool for students studying mathematics, engineering, and various scientific disciplines.

You can download the PDF version of this antilog table: Antilog Table PDF

Read More,

• Logarithms
• Logarithm Formulas
• Logarithmic Differentiation

Solved Example of Antilog Table

Example 1: Calculate the antilog of 2.7845.

Solution:

Certainly, let’s go through the steps to calculate the Antilogarithm for the given logarithm 2.7845 using the method you’ve provided:

Step 1: Given logarithm: 2.7845.

Separate the integral part (characteristic) from the fractional part (mantissa):

• Characteristic: 2
• Mantissa: 0.7845

Step 2: Find the equivalent value of mantissa using the Antilog table. Look for the row number that corresponds to 0.78 in the Antilog table. Select column number 4. Let’s say you find the value 6081 in this row and column.

Step 3: Proceed to the mean difference column. Use the 0.78 row again and get the appropriate value in column 5. Let’s say the value in this case is 7.

Step 4: Add the values discovered in steps 2 and 3. Add 6081 and 7: 6081 + 7 = 6088.

Step 5: Insert the decimal point. You must multiply the characteristic value by 1. You now have 3. Then, after 3 digits, add the decimal point to obtain 608.8.

Result: The Antilogarithm of 2.7845 is approximately 608.8.

Example 2: Use the antilog formula and a calculator to check the answers in Example 1.

Solution:

By Antilog formula, antilog(x) = 10^x

Antilog(2.7845) = 10^2.7845 = 608.8

A calculator is used to verify the answers.

Example 3: Calculate antilog(4.4771).

Solution:

By Antilog formula, antilog(x) = 10^x

antilog(4.4771) = 10^4.4771

antilog(4.4771) ≈ 26645.82

So, Antilog(4.4771) is approximately equal to 26645.82.

Antilog Table – FAQs

1. What is the Anti Log?

The anti-log is the inverse of a logarithm, used to find the original number from its logarithmic value.

2. What is Antilogarithm Table?

An Antilog table is a mathematical and technical reference tool for determining the values of Antilogarithms, which are the inverse operations of logarithms. It gives pre-calculated exponential values for specified logarithmic inputs, making difficult calculations easier before the digital age.

3. How to Use Antilog Table?

Separate the provided logarithm into its characteristic and mantissa portions before using an Antilog table. In the table, identify the row for the characteristic and the column for the closest mantissa value. The intersection of the row and column yields the Antilogarithmic value.

4. How to Find Antilog?

To find antilog we can use the formula that is given as: antilog(x) = 10^x

5. Why Do We Use Anti Logarithm Table?

As all the complex calculations in ancient times were done manually, antilog tables are used to make our calculations easy and quick.

6. What is the difference between Natural Logarithm and Common Logarithm?

Because of their various bases, natural logarithms (base e) and common logarithms (base 10) have unique Antilog tables. When utilising Antilog tables, make sure you’re using the correct table for the logarithm base you’re dealing with.

7. Where can you Download Antilog Table PDF?

You can download the PDF version of this antilog table: Antilog Table PDF.

8. What is Antilog of 15.6?

The antilog of 15.6 is 3.981 × 10¹⁵ as antilog(15.6) = 3.981 × 10¹⁵.