CBSE Class 11-science Answered

The logarithm of any number is a combination of two parts. These are Characteristics and Mantissa. Characteristic is the name for the term before the decimal and Mantissa is the name for decimal term. These log tables are used always to find out the Mantissa. Characteristic can be found out by using the simple rule, i.e.

Characteristic = (no. of digits before decimal) – 1

E.g. in 236, the number of digits are 3 because the no. can be written as 236.0 and hence characteristic is 2 and in 0.641, the number of digits before decimal is 0, and hence the characteristic is -1 and written as ?. Characteristic can be negative in certain cases but Mantissa can never be negative.

Now if we have to find the logarithm of 3.14 then as the no. of digits before decimal is 1 so its Characteristic will be 0. Now for Mantissa look at the first column of log table at 31 and then note down the number given in the fifth column of the row of 31. We are looking at fifth column because it is the one with the digit 4 on the top.

Therefore log of 3.14 = 0.4969