Logarithm is the mathematical tool or function. By the use of logarithm, we find the power of the base to find out the required result. Like, if we need to find out the power of 4 to get the result 64, its clear that we need 4x4x4 i.e. 43. Here 4 is the base, 3 is the power and 64 is the result.


Simply, we can say that by the use of logarithm, we get the answer of the question that " What exponent do we need for one number to become another number"?

Example: How many 3s do we multiply to get 81.Solution: We need
3 x 3 x 3 x3 = 81, so if we multiply 3 four times with itself, we get 81. Hence logarithm is 4.

To know about logarithm, first we know about exponents.
Exponents: Exponents and logarithm are opposite of each other, just like
multiplication and division. Exponents undo logarithm. Technically we say, exponents are inverse of logarithm.
Example: xa = y where a is the exponent of base x.

Exponents indicates how many times we use the number in multiplication. This is a quantity indicates the power.
Example:
24 = 16, so we multiply 2 four times with itself to get 16 (i.e. 2 x 2 x 2 x 2)
Here 4 is the exponent and 2 is the base.




Exponent is a variable. Exponents are positive and negative numbers, complex number, rational numbers etc. In an expression they are denoted by superscripts.

Logarithm: If we have the expression ax = y, here a is the base, y is the result
and x is the exponent.
Now we can say that " logarithm of a number y with the base a is the power (exponent) to which a has to be moved to get y". Generally we denoted logarithm by log.

Now if we have 24 = 16
or 2 x 2 x 2 x 2 = 16
Now we can write log216 = 4, so we say log base 2 of 16 is 4.

So to conclude, in logarithm, basically we deal with three things/ terms:
  • Base: The number we are multiplying.
  • Exponent: How many times we use the number to multiplication.
  • Result: The number we want to get i.e. the result we want to get.
Example: What is log6(216) = ?
Solution:
We are trying to know about " how many 6s need to be multiplied
together to get 216".
So, 6 x 6 x 6 = 216, we need three 6s.
Then log6(216) = 3
In other words the log of y to the base a is the solution x of the equation