How to calculate Logarithm of a number

Priyanka Rana
25 Mar 0 0

Practical calculations need to be done using log tables. In order to do so, here are some important formulae.

log(mn) = n log(m)

log(m×n) = log(m) + log(n)

log(m/n) = log(m) - log(n)


The log of any number contains two parts, one before the decimal, called Characteristic and the other after the decimal, called Mantissa.

It is only the Mantissa which we get to know from the log table. The characteristic is found by the rule that it is always less than 1 from the number of digits before the decimal of any number.

Eg: in 980, the number of digits are 3 and hence the characteristic is 2. In 0.486, the characteristic is -1 as there are no digits before decimal. (characteristic can be negative but mantissa is always positive.)


To find the log of 3.14, the most common factor in the calculation, its characteristic is 0. Now for the mantissa, put your finger on the first column of the log table at 31 and then note the number in the 5th column (the column with 4 at the top) of the row 31. Therefore, log(3.14) = 0.4969.

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