Logarithms Last Updated : 07 Apr, 2025 Comments Improve Suggest changes Like Article Like Report 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 bx = 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: logb(y) = x. And it is read as logarithm of "y" to the base "b".Example:If 23 = 8, then, log2(8)=3If 51 = 5 then, log5(5) = 1 Also, logarithm of 1 in any base is always 0 as a0 = 1 or loga1 = 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 BeginnersThis section introduces the basics of logarithms, their rules, properties, formulas, and how to use log and antilog tables.LogarithmNatural LogLog vs ln (Natural log)Log RulesLogarithm FormulasChange of Base Formula in LogProperties of LogarithmsLog TableAntilog TableLogarithmic FunctionLogarithmic EquationsApplication of LogarithmLogarithm Practice QuestionsPractice and test your understanding of logarithms with quizzes, MCQs, and problem-solving exercises.Quiz about LogarithmLogarithm MCQsLogarithmic Functions Practice ProblemsLogarithm for Aptitude PreparationPrepare 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 QuestionsLogarithms for ProgrammersLearn 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 ProgrammingLog functions in PythonNth root of a number using logCube root of a number using log function Comment More infoAdvertise with us Next Article Laws of Logarithms A ashutoshunfc Follow Improve Article Tags : Mathematics School Learning Tutorials Maths-Categories Logarithms Math Tutorials +2 More Similar Reads Logarithm 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 bx = 3 min read Laws of Logarithms The logarithm is the exponent or power to which a base is raised to get a particular number. For example, 'a' is the logarithm of 'm' to the base of 'x' if xm = a, then we can write it as m = logxa. Logarithms are invented to speed up the calculations and time will be reduced when we are multiplying 4 min read Log Rules Logarithm rules are used to simplify and work with logarithmic expressions. They help relate logarithms to exponents and make complex calculations easier.A logarithm is the inverse of an exponent. It answers the question: "To what power must a base be raised to get a certain number?"Out of all these 7 min read Logarithm Formula Logarithm is defined as the power to which a number is raised to yield some other values. Logarithms are the inverse of exponents. There is a unique way of reading the logarithm expression. For example, bx = n is called as 'x is the logarithm of n to the base b.There are two parts of the logarithm: 6 min read Continuity and Differentiability of Logarithmic Function The word continuity means something which is continuous in nature. The flow of water is continuous, time in real life is continuous, and many more instances show the continuity in real life. In mathematics, the Continuous function is the one which when drawn on a graph does not show any breaks and i 5 min read Derivative of Logarithmic Functions Derivative or Differentiation of Logarithmic Function as the name suggests, explores the derivatives of log functions with respect to some variable. As we know, derivatives are the backbone of Calculus and help us solve various real-life problems. Derivatives of the log functions are used to solve v 10 min read Logarithmic Differentiation Method of finding a function's derivative by first taking the logarithm and then differentiating is called logarithmic differentiation. This method is specially used when the function is type y = f(x)g(x). In this type of problem where y is a composite function, we first need to take a logarithm, ma 8 min read Log Table A Log Table in math is a reference tool to ease computations using logarithmic functions. It usually provides pre-computed logarithm values for various integers, commonly in a base like 10 or the natural logarithm base (e.g., ≈ 2.71828). Log tables allow users to obtain the logarithm of a given numb 9 min read Antilog Table Antilog Table in math is a refrence tool used to reverse logarithmic computation and retrieve the original number from its logarithmic value.It typically provides a pre-computed antilogarithm value for various logarithmic inputs, commonly in base 1o or natural logarithm base( e.g ≅ 2.71828)Antilog t 7 min read Change of Base in Logarithim The change of base formula is a useful concept in mathematics. That allows you to convert a logarithm from one base to another. Change of base formula in logarithm allows us to rewrite a logarithm with a different base. It allows us to compute logarithms using calculators or computational tools that 4 min read Difference Between Log and Ln Logarithms(log) and natural logarithms(ln) are fundamental mathematical concepts that simplify complex calculations involving exponential relationships Logarithms are essential for solving equations where an unknown variable appears as the exponent of some other quantity. A logarithm can have any po 3 min read Like