Square Root | An Exciting Outcome

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Everyone knows what a square root is for and what it does to a number.

But have you tried multiple square rooting ?

What do I mean?

Let's take an example.

Start with a number, say, 3.

i)  Square root this 3.
ii) You will get a number after step one.
iii) Square root this new number again.
iv) Continue the steps above and look closely at the number.

Findings: 
You will notice that the number after multiple square rootings, will give you closer and closer to or approaching the number "1".


Now let's start with another number. This time, let's choose, 0.4

After doing the same procedures, you will again notice that the answer is getting and approaching the number "1"!

Amazing isn't it?

What other wonders can you find from this Square Root maths operator?
Share with me in the comment section.

Maths is interesting.........

:D

Logarithm Operation Explained (2)

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Logarithm operator exists as a mathematical tool to allow us to convert a number to another form in terms of base and power.

Can you make 0.5 in terms of 10^y or 5^y ?

The above is a maths question that can use logarithm to solve.

The application requires the Power rule that states that log_kD^m is equivalent to mlog_kD.
With that knowledge, to convert the above question of 0.5 to various base, we simply log the 0.5 to its respecive base.

Let's go for the base 10.

Original:   0.5 = 10^y

Performing "log" on both sides:
log₁₀ 0.5 = log₁₀10^y 
-0.301      = y  log₁₀10
-0.301      = y

or another way to put the outcome is 0.5 = 10^-0.301

We have managed to convert the original number of 0.5 to one with base 10 and a power (index) of "-0.301".

We can also similarly do the same for a base of 5. =>  0.5 = 5^y
Here we just "log" to base 5.

log₅ (0.5) = log₅ 5^y = y
-0.431       = y

Thus 0.5 = 5^-0.431

From the 2 examples above, you can see the wonders of having logarithm as a conversion tool.
Once you understand this principles, you will appreciate logarithm.

Cheers!
:D

Logarithm Operation Explained

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Everyone knows what happen when we add a number to another.

We also know what happen when we do subtraction.

There is also no problem with multplication or division of numbers.

These are all simple mathematical operations that are basic.

What about doing a logarithmic operation in math?
This is a slightly complex but interesting question.

When we do a logarithmic operation on a number, what we actually do want out of the mathematical process is the power or index with reference to a base number.

10⁵ has a base number of 10 and index of 5.


Doing a "log" of the above will reveal an answer of 5.
This is the power after doing a "log" operation.

Thus, when anyone does a logarithmic operation on a number (or expression), he is trying to find the index with respect to a base reference.

log 10⁵ = 5.

Note: 
Full written log expression is "log_kP".   When the "k" is left out, it implies that k = 10.
And log 10 = 1.

I hope the above can explain why we do logarithmic operation and its significant.

There must be a reason for each math operation, otherwise we will be learning and doing some insane process on earth!

Maths Is Interesting!

:-D

Math Challenge 19

Math does not involve variables that we can see only.

There are the logical deduction type whereby you have to visualise and come out with an answer.

Below is one good example that I would like it to be a challenge.
(Don't be frightened by this, it is just for fun.....)

Above you will find a stack of cubic boxes. There are the blue and the yellow cubes.

Question:
What is the least quantity of blue boxes must we use in order to hold the yellow boxes in the same place?

You may present your answer and how you arrive at the answer in the comment section.

Thanks for trying. And I am waiting for that interesting mathematical deduction...

Maths Is Interesting!

Cheers :-D