LOGARITHM Meaning and
Definition
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A logarithm refers to a mathematical function that is used to determine the exponent to which a fixed base must be raised to obtain a given number. It is essentially the inverse operation of exponentiation. The logarithm of a number is denoted by the symbol "log" followed by a subscript indicating the base of the logarithm.
In a logarithmic equation of the form y = log(b, x), where "b" is the base and "x" is the argument, the value of "y" represents the power to which "b" must be raised to obtain the value "x". For example, if we have y = log(10, 100), this equation represents that 10 raised to the power of "y" equals 100, and in this case, "y" would be equal to 2.
Logarithms play a crucial role in many areas of mathematics, science, and engineering, particularly in equations involving exponential growth or decay. They are highly valuable for simplifying complex calculations by transforming exponential equations into linear equations, making them more manageable to solve. This property makes logarithms useful in fields such as calculus, statistics, physics, and finance.
Common bases for logarithms include 10 (log base 10 or common logarithm) and the number "e" (log base "e" or natural logarithm), where "e" represents Euler's number, a mathematical constant approximately equal to 2.71828. Logarithms are also applicable to negative numbers, complex numbers, and even fractions, extending their utility to a wide range of mathematical operations.
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A system of artificial numbers which greatly facilitate certain calculations, in such a way that while the natural numbers increase in geometrical progression, their logarithms increase in arithmetical progression only; thus, while 1, 2, 4, 8, 16, 32, 64 are natural numbers, 0, 1, 2, 3, 4, 5, 6 are their corresponding logarithms.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
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Etymology of LOGARITHM
The word "logarithm" is derived from two Greek words: "logos" meaning "ratio" or "proportion" and "arithmos" meaning "number". In the 17th century, the Scottish mathematician John Napier coined the term "logarithm" to describe the mathematical concept he developed. The logarithm is a mathematical function that determines the exponent to which a base must be raised to obtain a given number.
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