Logarithm

Logos meaning 'ratio' and arithmos meaning 'numbers' in latin together form the word which is very commonly used in Maths and extended to Physics and Chemistry of our highschool and college life.

(I just felt the importance of specifying the fact that the word 'Log' which is used a lot in this chapter has no relation whatsover to a certain brown thing thrown into fire... Mathematicians didn't name it 'log' cause they wanted to shove it into the fire after all, who knew! )

From my previous physics and maths blogs, you would have noticed the tendency of operations and properties to always have an alter ego. If they do a certain function, there will definitely be another operation which does the exact opposite of what it does.

(Leave it to physics to be self-destructive)

In the same lines, we have previously learnt about exponents or powers, Logarithm is the exact opposite of this operation

A quick recap on exponents-

Exponents helps us express repeated multiplication. If a number is said to be raised to its nth power, that means it is multiplied n times :

Exponents find out the final answer after the repeated multiplication, Logarithms ,on the other hand, figures out the power with which a particular number should be raised to get the result -- it finds out the 'n' considering the above example.

Another example,

Here, 'a' is the BASE

'X' is the ARGUMENT

'n' is the EXPONENT

Logarithm tells us to what power 'a' should be raised to get the value X

(Simple isn't it?)

Limitations Of Logarithm --

Just for example ( we all like the rebelious adrenaline rush on breaking rules don't we? So for the purpose of the readers, let's assume exactly what the mathematicians have asked us not to do)

Let's take (base) a = -4 (which is lesser than 0) and take the 1/2 root of this number

which is not possible. Squares of a number are always positive, hence number under square root should also be positive.

Hence the bases can't be negative.

Now lets consider 0

0 raised to the any power, will still give zero, There is no possible way IN THE UNIVERSE, that zero raised to a number can give us 2 or 7 (No, I am not being melodramatic 😬)

So, that cancels out zero

Next left is one

We know 1 raised to any number will give us one

Hence,

We can't raise one to any number to get 32, hence just like 0, we avoid taking one as the base.

The value of Argument depends on base,

We know a positive non-zero number raised to any degree will still give us a positive non-zero number. (Image 3 check these examples our for more clarity)

But, in the second case, we include 1 in the Argument as anynumber raised to 0 will always give us 1, hence it can be counted.

Okay, let's face it, We failed miserably to prove the past mathematicians wrong ( I can hear their evil laughter too)

From now on, let's stick to the rules they already gave?

So, these are the basic formulaes with which we can complete any question thrown to you straight out of the fire... (。・・)ノ

Few examples:-

Insert any value for these formulas and tada!

That's all folks! I am keeping it a trend to always end my blogs with jokes, so let's keep up with the traditions