Introduction of antilog Table and how to use it?

An antilogarithm table is a mathematical table used to calculate antilogarithmic values. The anti-logarithm is the reciprocal of the logarithm. Simply put, if you know the logarithm of a number, you can use the antilogarithm table to calculate the actual value of the number.

Use the antilogarithm table to easily perform mathematical calculations without a calculator. Inverse logarithm tables are most commonly used in computers and calculators. These are especially useful in fields such as engineering, finance, and science where logarithmic functions are commonly used.

Although the antilogarithm table is not widely used today, it continues to be a useful tool in understanding logarithmic functions and for historical and educational purposes. To better understand the usage of the anti-logarithm table, we will now discuss an example of its use.

In this article, we will discuss the basic definition of its formula with the help of an example.

Definition of antilog table:

An antilogarithm table is a mathematical method of calculating the (antilogarithm or antilogarithm) of a number. That is, it is used to calculate the actual value of a number obtained by taking the logarithm of another number.

Use the table of exact numbers for convenience. First, calculate the characteristic of the numbers you want to solve for the antilogarithm, then find the comparable rows in the table. Then compute the mantissa of the numbers in the left column and read the corresponding values ​​of the antilogarithm from the same row.

The inverse logarithm table shows positive or negative values. The antilogarithm is the antilogarithmic process function. If log a = b, then a = antilogarithm (b). As the logarithm goes from one side of the equation to the other, it becomes an antilogarithm. 

Log a = b → a = antilog (b)…. (A)

The logarithmic equation can be used to transform the logarithmic equation into an exponential equation. Therefore

Log a = b→ a = 10^b… (B)

From equations (A) and (B), we can say that the antilogarithm (b) = 10^b. Example:

Antilog (3) = 10³ = 1000

These values are commonly recorded in a table format, where the left-hand column shows the mantissa of the number, and the top row shows the characteristic or exponent of the number.

How to use an antilog table?

An Antilogarithm table regularly calculates the logarithm of some values. As known, the logarithm of any number can be studied (characteristic plus mantissa), where the characters can be either positive or negative whereas the mantissa should constantly be positive.

 Suppose we remember how to separate the characteristic and mantissa from the logarithm of a number. Generally, so be careful while solving in this method of negative numbers (in this process of negative numbers we add and subtract 1 to make mantissa positive).

Log of values	Characteristic + Mantissa	characteristic	Mantissa
5.34566	5 + 0.34566	5	0.34566
0.0034	0 + 0.0034	0	0.0034
-5.2678	-5 – 0.2678 = (-5 -1) + (1-0.267) = -6 + 0.733	-6	0.733
-1.78	-1 -0.78 = (-1 -1) + (1-0.78) = -2 + 0.22	-2	0.22

 

How to Find Antilog of Number without using Antilog Table:

An antilog table is a mathematical table used to calculate the value of an antilogarithm. We use the antilogarithm formula to be antilog (a) = 10^a. Now, this formula can be used without a calculator only when a is an integer. If “a” is not an integer, we will have to use a calculator to compute 10^a.

Table:

Here’s a table showing some common values of the anti-logarithm function (with base 10):

Logarithmic Value	Method	Anti-Logarithmic Value
0	100	1
1	101	10
2	102	100
3	103	1000
4	104	10000
5	105	100000
6	106	1000000
7	107	10000000
8	108	100000000
9	109	1000000000

How to calculate antilog?

In this section, we’ll take some examples to calculate antilog.

Example 1:

Calculate antilog of (3.3010)

Solution:

To get Antilog (3.3010)

Step 1:

Characteristic Part = 3 and Mantissa Part = 0.3010

Step 2:

Using the logarithm table on row 0.30 and then using column 1 gives 2000.

Step 3:

Calculates the value from the middle difference column of rows 0.30 and column 0 returns the value 0.

Step 4:

Adds value incrementally 2 and 3, 2000 + 0 = 2000.

Step 5:

Determine the number of decimal places. Since we know the characteristic part is 3, we need to add 1 to this, so we get the value 4.

Example 2:

To calculate the antilog of 3.542

Solution:

Given the antilog of 3.542

Step 1:

Suppose, we want to calculate the antilogarithm of 3.542.

Step 2:

To compute the characteristic and mantissa of the logarithm in the antilogarithmic table. The feature is the integer to the left of the decimal point and the mantissa is the fractional part to the right of the decimal point. Generally, the characteristic part is 3 and the mantissa is 0.542.

Step 3:

Find the row corresponding to the characteristic in the inverse logarithm table. To find rows equal to 3.

Step 4:

Find the column corresponding to the first two digits of the mantissa in the antilogarithm table. The first two digits of the mantissa are 54, so look for the column corresponding to 54.

Step 5:

Find the value at the intersection of the row and column identified in steps 3 and 4. This value is the inverse logarithm of the starting logarithm. The intersection value of row 3 and column 54 is 3.53.

Step 6:

So, the Aantilogarithms of 3.542 is 3.53.

Summary

In this article, we have discussed the definition of an antilog table, the uses of an antilogarithm table, and antilogarithm numbers without using an antilogarithm table through the help of examples. Moreover, you can completely understand this article, anyone can easily solve any problem of the antilogarithm table.