## Monday, 1 July 2013

### LOGARITHMS

LOGARITHMS give you the 'X Co-ordinate' of a graph, if you know the slope of the graph(tan 0) and the corresponding Y Co-ordinate.

EXAMPLE

|||| Imagine a car moving with a speed increasing at a rate of 10 m/s  with every tick of the clock.

|||| i.e

|| In the 1st second,

the speed  by the car is 10 m/s,

|| In the 2nd second

The speed of the car jumps to 100m/s

|| In the 3rd second

The speed of the car jumps to 1000m/s and so on...................

|||| So its basically a crazy car.

|||| Now lets say our need is to find out how much time did it take for the car to reach a speed of 500m/s in this whole journey?

Simple......simply take log10(500) which = 2.3 seconds.

|||| Yes, it took just about 2.3 seconds for our crazy car to reach a speed of 500 m/s.

WHY IS log (A X B) = log ( A ) + log ( B ) ?

|||| Imagine an elastic. Now lets say you stretch this elastic first 3 times its original length and from there  4 times more its stretched length.

|||| So the elastic is actually stretched 4 x 3 = 12 times.

|||| Now the force required to stretch this string is calculated by log(4 x3)

|||| Now force required    = Force required to   + Force required to stretch the
required stretch the     stretch the string      string 3 times from there.
string 12 times              4 times

|||| In other words

Log (12) = log ( 4 ) + log ( 3 )

or

Log( 4 x 3) = log (4 ) + log (3)

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AVAILABLE FOR PURCHASE FOR 5\$ (INR 300) HERE (PDF)

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I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it.

Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life.

Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most.
The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.

Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.

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CONTACT
binnoypanicker@gmail.com

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