CALCULATION MADE EASY

Long ago, In astronomical calculations, people had to multiply and divide large numbers. They wanted to find an easy way out. And Napier's work in this direction gave birth to Logarithms which made computation easier. Let us explore the concept.
Consider, 1,2,3,4,5,6
This is the sequence of natural numbers and also called arithmetic progression (A.P)
2,4,8,16,32,64...
In the above series, the ratio between successive number is 2. And it is called Geometric progression(G.P).
Now, if you want to multiply or divide the numbers in G.P, Add or subtract corresponding number in A.P and then find the corresponding number in G.P for that answer.
Example:
To multiply 4 and 16, in G.P
Add 2 and 4 in AP
2+4 = 6
Corresponding number for 6 in GP = 64
verified
4* 16 = 64
To divide, subtraction should be followed.
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So multiplication and division has been reduced to simple operations addition and subtraction.
We can understand
2^A.P = G.P Where 2 is ratio in G.P
eg: 2^3 = 8
Here we can treat A.P as the logarithm of G.P and 2 as the base.
Using the above technique and formula, we can create table of logarithms for all numbers and make the calculation easy. Here we are using the base 2.
But Euler's number e= 2.71... can be used as the base. Since, 'e' appears everywhere in natural growth and decay, we will get natural logarithm.
Even though, calculators and computers rendered logarithms obsolete, it still reign as an important mathematical function.
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