 # Antilog

Updated: 19 Aug 2023

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An anti-logarithm, often called the “antilog,” is the inverse operation of finding a logarithm. The logarithm of a number to a specific base, the anti-logarithm, allows you to find the original number.

## Definition of Antilog

If we have \log \ x=y , then x is the anti-logarithm of y and is written as x=anti-log \ ⁡y

## Antilog Table

An antilog table is a reference table used to find the anti-logarithm, the inverse operation of finding the logarithm. In mathematics, logarithms are used to solve exponential equations, and anti-logarithms are used to find the original values from logarithmic values.

### Parts of Anti-Logarithm

An Antilog table is divided into three parts.

#### Main Column

The first part of the table, the main column, contains numbers from .00 \ to \ .99

#### Differences columns

The second part of the table, called differences columns, consists of 10 columns headed by 0, 1, 2, …. 9 .

#### Mean Differences

The third part consists of small columns known as mean differences headed by 1, 2, 3, … 9 .

### How to use Antilog Table

• Separate the characteristics and mantissa.
• To find antilog, see Mantissa in Antilog Table.
• First, take the two digits (along decimal point) of the number whose antilog is required and see it in the row of the main column of the log table.
• Proceed horizontally along the selected row till the column headed by the third digit. The number under this column is the value of mantissa.
• Now see the fourth digit in the mean differences columns of the same row and add to the value of mantissa found in the second column.

## How to find the Antilog

• Seperate the characteristics and mantissa.
• See Mantissa in Antilog Table.
• Find the value of mantissa.
• Write this value in Scientific Notation.
Antilog=value \times 10^{char}
• Convert the scientfic notation to standard form.
##### Find the antilog of 2.3456

Solution:
Here the digit before the decimal point is Characteristics:
Characteristics=2
And \ Mantissa= .3456

• To find the anti-log, we see Mantissa in Antilog \ Table.
• Take the first two digits, i.e. .34 and proceed along this row until we come to the column headed by the third digit 5 of the number, which is 2213 .
• Now take the fourth digit, i.e. 6 and proceed along this row which is 3 .
• So to find an anti-log, write it in Scientific form like
anti-log⁡ \ 2.3456=2.216×10^{char}
anti-log \ ⁡2.3456=2.216×10^2
• Write in Standard Form
anti-log \ ⁡2.3456=221.6
##### Find the anti-log of \overline{2}.2508

Solution:
\overline{2}.2508
Let \log \ x=\overline{2}.2508
Taking anti-log on B.S
Antilog⁡ (\log⁡x )=Antilog (\overline{2}.2508)
⁡x=Antilog (\overline{2}.2508)
Now
Characteristics =-2
Mantissa =.2508
So:
x=1.781×10^{-2}
x=0.01781

R.W
1778+3
= 1781

## Anti-log – MCQs

1. The anti-log 1.2508 is
O 1.781
O 17.81
O 1781
O None of these

17.81
Explanation:
See Ex # 3.4
Q No. 1
Part No. (i)

2. The anti -log 0.8401 is
O 6.920
O 69.20
O 6920
O None of these

6.920
Explanation:
See Ex # 3.4
Q No. 1
Part No. (ii)

3. The anti-log \overline{2} .2508 is
O 1.781
O 17.81
O 1781
O 0.01781 