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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