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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 .
  • Now add 2213+3=2216
  • 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
Show Answer

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
Show Answer

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
Show Answer

0.01781
Explanation:
See Ex # 3.4
Q No. 1
Part No. (iv)


jawad khalil

jawad khalil

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