Power Law of Logarithm Explained

Logarithm study has a few formulae that are important and key to solving math questions.

By remembering them , you will be in line to solve logarithmic problems and, maybe, fast too.

However, what if you forget them?
Does it mean that you are not able to solve the question regardless of speed?

Do not despair.
As long as you are able to manage the 2 basic laws in logarithm, you are safe.

The product law and the quotient law are must for any students.

Why do I say that?

Let us take the Power Law and do a review.

n log x = log X ⁿ

Why is it so? What if you forget this law? Any problem?

These are the very queries any new learners exposed to logarithm will ask.

First allow me to go through the product law of logarithm.
log (XY) = log X + log Y

Here you see that the product of "X" and "Y" in logarithmic operation, becomes a "sum"of the individual logarithms.

4 log Y = log Y + log Y + log Y + log Y (adding up 4 of the log Y)

Using product law, you know that these 4 terms can be combined to log (Y x Y x Y x Y).

log (Y x Y x Y x Y) = log Y⁴

Now, you see, through the product law, you are able to equate the 4 log Y into log Y⁴ ,
meaning, 4 log Y = log Y⁴.

You see that you did not utilise the Power Law here,and yet is able to form this formula!
Amazing isn't it.

What is the message here?
The message is that, when you have the basic understanding in logarithmic principles, you will be able to twist and turn any given problems to come out a solution.

You had used the basic product law to discover this unique Power Law.
It is similar to other laws and also can be expanded to cover other maths topics too.

Do enjoy maths.
Do discover more exciting twists it presents wwith a bit of thinking.

Happy learning :-)

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Learning Math Topics in Isolation

Learning encompasses linking with other area and related topics.

Learning thing with disregard for other is alright for the sake of triggering the mind. But does it benefits more if linked to others?

Does indices related to quadratic equation?
Does multiplication relates to addition?
Does complex number relates to algebra?

All the above questions are common in the mind of a math learners.
If you do not have these questions along the learning phase, something is very wrong.

Learning math in isolation is similar to living in an isolated island all by yourself.
You do not know what is happening in the world.
You do not know if there is famine somewhere, or swine flu going round, or a plane crash near you.

Math has to be done with linkage to many other mathematical topics. It cannot be done in isolation.

Math is a tool that solves real-life problems. With mastery of various mathematical concept and relation among them, you will be better prepare to solve more problems.

Many a time, you will come across students who just study topical math without knowing that they can apply what have been taught to them previously.

They start fresh when a new topic is introduced.
Algebra is different from complex number.
The addition in complex number is done differently from that done in algebra. That's what they assumed, since the heading is different!

Interesting learning ways, right?

That is human nature, to be frank. Only when you are told, sometimes, otherwise you will not know it. Adults learn through experience that this assumption is pulling you down.

The ability to link many things together is a very beneficial skill to permanently internalise.
This does not point to math alone. Others apply.

Math can be tough if learned using an improper learning method.
One good technique is the linking technique where you will see yourself happily doing math, being able to apply and solve questions using previous and current taught concepts.
It motivates you.
This is the STARTING point if you are unaware. This is the point where it decides whether you can sustain math learning.

Learn wide and later deep into math. But start with the correct footing. Link as much to previous as possible. It will be a sure way to happy math doing.

:-) I like math!
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Counting Down With Base Eight

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Counting up is an easy task for anyone, even when the base is not ten.

You may refer to this link for counting (up) with base 8.

However, counting down may be slightly harder than normal, especially when dealing with another number base other than 10.

Let's try with base 8 for a start.

10
03 -
----
??
---

Here a count down of 3 from 10 is needed.

How do you go about it?

Thinking of the way base 10 subtraction was dealt with, this is similar.
After all maths is the same. It is the technique that is important.

When you encounter a " bring back" from the upper (rightmost) digit to the lower leftmost digit, you will, for base 10, add a 10 to the "ones" digit.

Here, with base 8, you will do likewise, except that now it is adding the number 8 to the leftmost digit.

Thus, 0 + 8 = 8.

And 8 - 3 = 5.

10
03 -
----
05 (Answer in base 8).
---

There is nothing difficult if you look at the technique or concept in counting up or down.

Maths is just playing with methods to resolve numerical issues.

The above is a good example. Hope you agree?

Have fun counting in other number base.
Cheers!

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Careful With The Use of 2 and Z in Maths

Mistakes are normal in maths. This is during the learning stages.

It will not be acceptable during tests and examinations. This everyone knows!

But human do make mistakes. This is a fact. Therefore, we have to know our weakness and avoid moving towards it (them).

A very common mistake made while doing maths is to use the variable "Z". From the writing, you can see that it is very similar to the number "2".

During examination, we are tensed up and our mind may not see what the eyes received.

2Z may end up as 22 finally. This "22" will then be used for computation and of course results in a BIG shock!

Thus knowing this danger, avoid using variables that are close to number in writing, unless stated by the maths question itself.

Do not choose a similar looking variable and end up with disappointment.

"b" and "6", "l" and "1" or "S" and "5". These are dangerous combination.

Thus look carefully when dealing with these numbers and variables.

Do not cause unnecessary mistakes. Save your effort to deal with better challenging thinking.

:)

Counting With Base Eight

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Number system has an important factor attached to it.

It is the base of the number.

The base defines the quantity of item (in this case, the counted number) before the sequence repeats.

Take for example, base 8.
The count is: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12 ....., 17, 20, 21, 22, 23,.......

The number "8" does not appear in the base 8 number system.

Once the 7 is reached, the next number increments to 10.
That is, the range is from 0 to 7 only.

How about the addition?

Example 1:

05
03 +
----
10
----

Since 5 + 3 exceed the maximum count of 8, the final added answer is 10, the start of next sequence.

Example 2:

14
05 +
----
11
----

It can be seen from the 2 examples above that the second digit in the addition is added with "1" after the first (right-most) digit shoots over "8".

This counting technique is nothing different from our normal base 10 (decimal) method of addition.

Thus, knowing the meaning of the base in the number system helps in proper counting, and includes addition and subtraction with the respective base.

It is nothing complex and abstract. Just counting with the correct quantity of number.

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Time Calculation May Not Be Easy

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Counting from 1 to 100 is normal for anyone. Just increment by 1. It's that simple.

But counting time may be another story for young math students.

Why is this so?

There is the seconds, the mintes, and the hours to handle. They differ by the umber 60.

The "carry over" through addition is the number SIX!

1 min 30 sec added by 40 sec gives .......

1 min 70 sec?

Here the 70 sec includes 60 sec + 10 sec. You need to understand that for time, 60 sec means one whole minute.
Thus, 70 sec = 60 sec + 10 sec ===> 70 sec = 1 min + 10 sec.

Therefore, 1 min 30 sec add 40 sec gives ==> 2 min 10 sec.

Compare this to adding 30 by 40. Answer = 70. No more analysis.

Time base on 1 hour = 60 min, 1 min = 60 sec concept.

To test true understanding of addition (and subtraction), time is a good gauge and tool to assess learners.

Test it on young kids today to annoy them... *#^&@!
Cheers!

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