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Logarithms - GeeksforGeeks

Laws of Logarithms

Logarithms

Last Updated : 07 Apr, 2025

In mathematics, a logarithm is the inverse operation of exponentiation. It is defined as the power to which the base number must be raised to get the given number.

Logarithms serve as mathematical tools that help simplify complex calculations involving exponential relationships.

If you know that b^x= y (where b is the base, x is the exponent, and y is the result), it means that you have to raise "b" to the power "x" to obtain the result "y", then by using logarithm we can say that the log of "y" to the base "b" is "x".

This can be written as: log_⁡b(y) = x. And it is read as logarithm of "y" to the base "b".

Example:
If 2³= 8, then, log⁡₂(8)=3
If 5¹= 5 then, log₅(5) = 1
Also, logarithm of 1 in any base is always 0 as a⁰ = 1 or log_a1 = 0(for a > 0).
Note : If the number is same as the base then the its log value will always be equal to one.

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Laws of Logarithms

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