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Why Do We Study Logarithms?

An insight to the history and applications of logarithms

Date : 16-05-2015

Author Information

Komal

Uploaded by : Komal
Uploaded on : 16-05-2015
Subject : Maths

Long before calculators were invented, the human race have been performing arithmetic operations (addition, subtraction, division, multiplication) on huge numbers. Scientists working in areas of research such as long distance navigation and astronomy constantly had to perform long, tedious calculations. So functions such as the trigonometric functions and logarithms were invented. They started out observing ratios and as a different way to view relationship of large numbers, and slowly made their way into these tedious computing tasks because of their usefulness! Here we give an example why: Imagine you have two big numbers A and B. Now, instead of multiplying them, you found a book containing a logarithmic table (in the olden days, they calculate log of huge numbers to high precision and publish them in a table form; today we just press the calculators) and knowing full well the operations of logarithms, you realized that log(A*B) = log(A) + log(B). The values can be looked up easily, and addition is WAY EASIER than multiplication! Indeed, that was how logarithms started out - transforming long multiplications and divisions into simple additions and subtractions. But why do we need them now? The reason why we need them now has not changed. We still use them in our computing tasks, but these tasks were hidden away behind the computers and calculators that we use them without knowing that they are there. Again you might wonder, "that still doesn`t mean I should learn them"! Rightfully so, but you see, the study of mathematics is not solely about learning useful formulas. In learning concepts like logarithms, indices, and trigonometric ratios, we - the math teachers - are trying to impart to you the logic and reasoning that goes behind the formulas and equations. In learning the rules and manipulating logarithms to prove identities or solve equations, you are exercising and stretching your mind, learning to recognize patterns better and learning to "move mathematical objects/symbols" around in your head. Everything is math is backed with reason, and the more you pay attention to the "how" of each step in solving an equation, the more you fine-tune the way you think and you speak in real life! (For more related posts, visit www.mathsplained.wordpress.com)

This resource was uploaded by: Komal