Antilog
Published: 19 Aug 2023
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.
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 $
Solution:
$ \overline{2}.2508 $
Let $ \log \ x=\overline{2}.2508 $
Taking anti-log on B.S
$ Antilog (\logx )=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 isO 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)
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- Be Respectful
- Stay Relevant
- Stay Positive
- True Feedback
- Encourage Discussion
- Avoid Spamming
- No Fake News
- Don't Copy-Paste
- No Personal Attacks
