Antilogarithm

• If $\log x = y$ then x is the anti log of y

• It can be written as x = antilog (y)

• The value of antilog of a number is find using antilog table similar to log table.

• If the characteristic of a number is positive than the antilog must have n+1 digits in integral part

  In simple words if the characteristic is positive then place the decimal from end to left

• If the characteristic is negative than the antilog must have n-1 zeros after the decimal point.

  In simple words if the characteristic is negative then place the decimal from start to left

Method of finding antilog

• First point out the characteristic and mantissa of the number i.e. antilog(2.4368) Characteristic = 2 Mantissa = 0.4368

• First two values represent the row of antilog table i.e. In .4368, .43 row

• Third digit represent the column i.e. In .4368, 6th column

• Find the value of intersection of .43 row and 6th column

• Fourth digit represent the column of Mean difference columns i.e 8th column of the mean difference

• Find the value of intersection of .43 row and 8th column of mean difference.

• Add both values

• If the characteristic is positive than n+1 rule and if negative then n-1 rule

Example#1

Find the value of antilog(3.5672)

Solution:

• Characteristic is 3 mantissa is .5672

• Intersection of Row .56 and column 7 gives 3690

• Intersection of row .56 and mean difference column 2 gives 2

• Add both $3690+2=3692$

• Characteristic is 3 so n+1 rule which says 3+1=4 digits before decimal point Means 3692.0 is the number

• $antilog(3.5672)=3692$

Example#2

Find the value of $\text{antilog}(\bar{2}.1324)$

Solution:

• Characteristic is $-2$ mantissa is $.1324$

• Intersection of Row $.13$ and column $2$ gives $1355$

• Intersection of row $.13$ and mean difference column $4$ gives $1$

• Add both $1355+1=1356$

• Characteristic is -2 so $n-1$ rule which says 2-1=1 zero after decimal point Means $0.01356$ is the number

• $\text{antilog}(\bar{2}.1324)=0.01356$