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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.

Logarithm For Beginners

This section introduces the basics of logarithms, their rules, properties, formulas, and how to use log and antilog tables.

Logarithm Practice Questions

Practice and test your understanding of logarithms with quizzes, MCQs, and problem-solving exercises.

Logarithm for Aptitude Preparation

Prepare for competitive exams with commonly asked aptitude questions on logarithms along with quick-solving tips and tricks.

Logarithms for Programmers

Learn how logarithms are used in programming, especially in time complexity and coding problems, with examples in Python.

Laws of Logarithms

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