Using Logarithmic Tables
Express the given number "n" in the form of m * 10p where 1≤m<10 and p is an integer(positive or negative whole number).
For example number 2 is expressed as 2*100
log n become equal to p + log m
log 2 becomes equal to 0 + log 2
p is called the characeristic and log m is called the mantissa. Mantissa is read from the logarithmic tables.
Logarithmic tables are show three sets of columns
i) the first set of column on the extreme left contains numbers from 10 to 99.
ii) in the seocnd set there 10 columns headed by 0,1,2,...,9
iii) after this, in the third set there 9 more columns headed by 1,2,3...9. These are known as mean differences.
As 1≤m<10, the mantissa is for a number between 1 and 10. Hence the interpretation of the first set of column in the table is 1.0 to 9.9, If you add the digit in the second set one more digit is added to the number. Which mean 1.0 becomes 1.01. If we add a digit in the third column on more digit is added to the number. Which means 1.01 becomes 1.011.
Hence log 2 = 0 + 0.3010 = 0.3010
How to see its antilogarithm.
Antilogaritm tables are written from .00. If mantissa of a logarithm is .00, then antilogarithm is 1.000
Antilogarithm of .3010 is equal to 2.000
As the characteristic of the number is 0 the number is 2.0*100. Which is equal to 2.
Suppose the problem is to find 2^(1/6). It is 2 to the power (1/6).
When we take logarithms, it becomes (1/6)* log 2 which is equal to (1/6)*(0.3010) = 0.0617 (rounded)
What is antilogarithm of 0.0617 = 1.153*100. = 1.153
So the answer of 2^(1/6) is equal to 1.153.