# How To Find Out The Anti Logarithm of a Given Number

What is Antilogarithm?

Antilogarithm is the reverse of logarithm.  Thus antilogarithm to logarithm is as division to multiplication.

For example, if log7 = 0.8451, then antilog 0.8451 = 7

Standard antilog tables are available for calculations.  We follow the rules given below for reading antilog tables:

(i)                  Read the antilog of mantissa only (i.e. of the decimal part); locating the four digits the way we did in reading mantissa from log tables in My Article : How to Find Logarithm of a Given Number.

(ii)                If the characteristic if positive say n, the decimal is placed after (n+1) digits in the value read.

(iii)               If the characteristic if negative, say n¯ , then (n-1) zeroes are placed before the left side of the number read; and then decimal point is placed.

(Here ¯ symbol is over the number i.e. n and is called bar)

For example:

Antilog 1¯.3478 = 0.2227

Antilog 2.7192 = 523.8

Antilog 0 = 1.000

Use of Logarithm

Logarithm is practically very useful in simplifying the complicated calculations.  Following examples will enable the students to use the log tables for that purpose.

Example1. Find the fifth root of 0.0076.

Solution. Let x=(0.0076)1/5

Taking log on both sides, we get

logx = 1/5log(0.0076) = 1/5(3¯.8808)

= 1/5 (5¯ + 2.8808) = 1¯.5762

Taking antilog on both sides, we get

x = 0.3769

Example2.  Simplify : x = 1.792 × 77.4 / (129.7)2/3

Solution.  Taking log on both sides, we get

logx = log1.792 + log77.4 – 2/3log129.7

= 0.2534 + 1.8887 – 2/3(2.1130)

= 0.2534 + 1.8887 – 1.4087

= 2.1421 – 1.4087 = 0.7334

Taking antilog on both sides, we get

x = antilog(0.7334) = 1.5413

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