Logarithm

Get The Basics Right!

Dealing with Logarithm is not as easy according to most that face it for the first time.

However ignoring and getting away with the subject without understanding the basics can be dangerous to say the least in future classes where it will come up in much more sophisticated form.

So take my word! Roll up your sleeve and get ready to take it head on. Of course you will find a lot of support here.

Let’s start by answering a few simple questions.

What is it?

Let me explain the definition above

Let’s take the number 8. The intention is to define the log of this number with respect to a certain base which is nothing but another number. Now for the purpose of this example I will take 2 as the base.

Thus the number is 8 and the base is 2. That means we need to find the logarithmic value of 8 with respect to base 2.

On revisiting the definition you will see that the definition says that we need to raise the base that is 2 to a certain power such that the resulting number is equal to 8. This power or exponent then will be the log value of 8 to the base 2.

Now 2 when raised to the power of 3 will give 8. Thus log of 8 to the base 2 is 3.

Therefore the entire stuff mentioned in the paragraph above can be rephrased as

x = by then,

y = logb(x)

Log Properties

Multiplication is a quicker version of addition. If you want to add 3 four times then you will get 12. The same result can be achieved by multiplying 4 to 3. This multiplication certainly seems to be much more sophisticated and faster than repetitive addition.

Exponents are a quicker way of doing multiplication. Multiplying 3 for fifteen times is same as raising 3 to the power of fifteen.

Similarly Log is a quick way of interpreting exponents.

Thus the logarithm properties are very much similar to the properties of exponents.


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