Logarithms — What, Why and How | Mathematics - Medium

Gaurav Goel, Storyteller, learner, thinker and a Software Professional dealing with Science and Engineering of Data explains, Understanding the intuition behind Logarithm Transformation and its use in Machine Learning.

A Logarithmic Spiral 
(Photo: https://commons.wikimedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg)

Science is the study of nature and a lot of scientific endeavors are about studying and measuring changes that occur in nature. We use numbers to express these measurements. If you think about “changes”, they can be only of two types — either a quantity increases (grows)or decreases(decays). The fundamental ways to capture these changes are the basic arithmetic operations of Addition, Subtraction, Multiplication, and Division.

Linear Growth or Decay

e.g Let's say a person is pushing a block with a force of 10 Newtons. Another person joins him and starts pushing the block, in the same direction, with a force of 5 Newtons. In this case, the total force on the block will add up and the result would be 15 Newtons.

In another case, assume that the second person starts pushing the block with a force of 5 Newtons but in the opposite direction of the first person. In this case, the resultant force will be calculated by subtracting the two forces.

Some quantities increase in the proportion to others. This is where the “multiplicative” effect comes to play...

But Why Logarithms?

It's much easier to relate to addition, subtraction, multiplication, and division….and in fact to some extent, even to exponentiation (think about population growth or COVID-19 infection spread). But why would someone care to compute the logarithm of a number? The simple answer is: Logarithm of a number gives a measurement of how “big” that number is in comparison to another number.

The human mind is capable of processing and comparing numbers that are on the same scale or similar scale. e.g let's say you are given the weights of different people(adults) of a group. Probably, everyone falls in the range of 40Kgs to 200 Kgs. We can visualize and compare these numbers with ease...

Logarithms may seem mysterious at first but if we try to understand the logic behind intuitively, it can open a whole new world of mathematical magic. I hope this article helped you to see some glimpse of this magic!
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Source: Medium