Logarithms

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
• Natural Log
• Log vs ln (Natural log)
• Log Rules
• Logarithm Formulas
• Change of Base Formula in Log
• Properties of Logarithms
• Log Table
• Antilog Table
• Logarithmic Function
• Logarithmic Equations
• Application of Logarithm

Logarithm Practice Questions

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

• Quiz about Logarithm
• Logarithm MCQs
• Logarithmic Functions Practice Problems

Logarithm for Aptitude Preparation

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

• Logarithm: Aptitude Questions and Answers
• Tips and Tricks for Logarithm Questions

Logarithms for Programmers

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

• What is Logarithmic Time Complexity?
• Logarithm Tricks for Competitive Programming
• Log functions in Python
• Nth root of a number using log
• Cube root of a number using log function

Logarithm - Definition, Function, Rules, Properties & Examples

Logarithm - Definition, Function, Rules, Properties & Examples

How to Use Logarithm(Log) Table with Examples