![]() ![]() In Logarithmic Equation we assume that the base of all the logarithmic terms is the same if no specific base is mentioned. Related Read: Logarithm Formulas Logarithmic EquationsĪn equation that involves logarithmic expression equated to any number or other logarithmic term is called Logarithmic Equation. The formulas for logarithm is tabulated below: Condensing LogĪ log can be condensed in the following manner just by following the reverse of the properties of log.Įxample: Condense log 2 + 3 log a + 2 log b Log(2a 3 b 2 ) = log 2 + log a 3 + log b 2 Log can be expanded in the following manner. Power Rule of Log : log x ab = b.log x a.Quotient Rule of Log : log x a/b = log x a – log x b.Product Rule of Log : log x ab = log x a + log x b.Expanding and Condensing LogarithmĪ logarithmic expression can be expanded and condensed using the following Properties of Log This rule states that the log of zero is not defined as there is no such number when raised to any power that results in zero. This is because any number raised to power 1 results in the number itself. This Property of Log states that if the base and augment of a logarithm are the same then the logarithm of that number is 1. This is because any number raised to power zero is 1. This property of log states that the value of Log 1 is always zero, no matter what the base is. Using these properties we can directly put their values in any equation. The expression can be given as:Īpart from the above-mentioned properties, there are some other properties of Log. Product rule of log states that if log is applied to the product of two numbers then it is equal to the sum of the individual logarithmic values of the numbers. The common Properties of Log are mentioned below: Related Read: Difference Between Log and Ln Logarithm Rules and Properties It is mostly used for solving large numbers and simplifying calculations. It is called natural log and is represented as ln x It is called a common log and is represented as log x Ln is the logarithmic expression at base e. Log is the logarithmic expression at base 10. The basic difference between log and ln is tabulated below: Log The natural logarithm is also written in the abbreviated form as ln i.e. The logarithm with base e, where e is a mathematical constant is called Natural Logarithm. The common logarithm is generally written as log only instead of log 10. The logarithm with base 10 is known as Common Logarithm. It should be noted that in both cases base is ‘a’ but in the log, the base is with the result and not the power.ĭepending upon the base, there are two types of logarithm If a n = b then log or logarithm is defined as the log of b at base a is equal to n. Logarithm is often referred to as the inverse process of exponents. In simpler words, we can say that if a and b are two numbers such that ‘a’ is raised to some power that gives the number ‘b’ then logarithm is used to find what is the power that ‘a’ must be raised to yield ‘b’. Logarithms are a way of determining the power to which a number is raised that gives a particular number. The creation of Logarithms is considered one of the important scientific discoveries in the history of science that were helpful in simplifying calculations of spherical trigonometry and celestial navigation. The purpose of the book was to help in the multiplication of quantities. In 1614 he presented his book named Canons of Logarithms which contained a table of trigonometric functions and their natural logarithms. ![]() The creation of logarithms is credited to a Scottish Mathematician John Napier.
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