Logarithm

First let's understand what Logarithm of a number is. The log of a number is the exponent or power or index to which the base of that number must be raised  to give you the number in question.

Example:

log1000 to base 10=3

When a log of a number is written without a base, its base is 10. Remember, we said that, the log of a number is the exponent or power or index of its base which will give the number in question. In this case the number is 1000 to base 10. So, the power to which 10 must be raised to give 1000 is 3. Therefore, the log of 1000 to base 10 is 3.

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Expressing exponential numbers in Logarithm:

Having understood the meaning of logarithm, it is easy to express numbers in Index form  in Logarithm.

Example:

Express 8²=64  in Logarithmic form.

                  Solution:

8²=64 

In the given number above, 8 is known as the base while 2 is the Index or exponent or power. The 2 is the Logarithm of 64 to base 8 and it is written as: