Logarithms and Types

Introduction:
          With the help of logarithm, we can abbreviate the process of multiplication and division.
Definition:-
If three numbers m, n and x  are related such that `m^n` `=x`
then n is called the logarithm of the number 'x' to the base 'm' and is written as
log_m  x  =  n

Meaning of Logarithms:

Let us take 2 ⁵ =  32, what power of 2 gives 32? The answer is 5

So the 5 is termed as exponent and 2 is termed as base

Means the exponent 5 is the logarithm of 32 to the base 2.

If 4 ² = 16, then logarithm of 16 to the base 4 is equal to 2   (  log ₄ 16   =  2)
4 ² = 16 is called as exponential form
log ₄ 16   =  2) is called as logarithm form.

Types of logarithm

1. Common logarithms.
Logarithms with base 10 are known as common logarithms. Whenever base of a logarithm is not mentioned, it is understood that it is base of 10. This is used for long arithmetic calculations.
2. Natural logarithms.
The logarithms to the base ‘e’ are called natural logarithms. The natural logarithm of x is denoted by lnx. Here e is Euler’s constant, an irrational number between 2 and 3.