**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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