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Bases Other than e and their Applications
Among all choices for the base (b), b = e, 2, and 10 are particularly common for logarithms.
Learning Objective

Distinguish between the different applications for logarithms in various bases
Key Points
 The major advantage of common logarithms (logarithms to base ten) is that they are easy to use for manual calculations in the decimal number system.
 The binary logarithm is often used in computer science and information theory because it is closely connected to the binary numeral system.
 Common logarithm is frequently written as "log(x)"; binary logarithm is frequently written "ld n" or "lg n".
Term

logarithm
the exponent by which another fixed value, the base, must be raised to produce that number
Full Text
Among all choices for the base b, three are particularly common for logarithms. These are b = 10 (common logarithm; see , b = e (natural logarithm), and b = 2 (binary logarithm; see . In this atom we will focus on common and binary logarithms.
The major advantage of common logarithms (logarithms in base ten) is that they are easy to use for manual calculations in the decimal number system:
Before the early 1970s, handheld electronic calculators were not yet in widespread use. Due to their utility in saving work in laborious multiplications and divisions with pen and paper, tables of base 10 logarithms were given in appendices of many books. Such a table of "common logarithms" gave the logarithmoften to 4 or 5 decimal places of each number in the lefthand column, which ran from 1 to 10 by small increments, perhaps 0.01 or 0.001. There was only a need to include numbers between 1 and 10, since the logarithms of larger numbers were easily calculated.
Because base 10 logarithms were most useful for computations, engineers generally wrote "log(x)" when they meant log_{10}(x). Mathematicians, on the other hand, wrote "log(x)" when they meant log_e(x) for the natural logarithm. Today, both notations are found. Since handheld electronic calculators are designed by engineers rather than mathematicians, they customarily follow engineers' notation.
Binary logarithm (log_{2} n) is the logarithm in base 2. It is the inverse function of
The binary logarithm is often used in computer science and information theory because it is closely connected to the binary numeral system. It is frequently written as "ld n" or "lg n".
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Key Term Reference
 binary
 Appears in these related concepts: The Cross Product, Defining Sex, Gender, and Sexuality, and Gender as a Spectrum and Transgender Identities
 e
 Appears in these related concepts: Derivatives of Exponential Functions, Natural Logarithms, and e
 function
 Appears in these related concepts: Solving Differential Equations, Functions and Their Notation, and Modal Mixture
 inverse
 Appears in these related concepts: Inverse Functions, Hyperbolic Functions, and The Law of Universal Gravitation
 inverse function
 Appears in these related concepts: Exponential and Logarithmic Functions, Finding Formulas for Inverses, and Inverses
 natural logarithm
 Appears in these related concepts: Logarithmic Functions, The Integral Test and Estimates of Sums, and Special Logarithms
Sources
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Cite This Source
Source: Boundless. “Bases Other than e and their Applications.” Boundless Calculus. Boundless, 21 Jul. 2015. Retrieved 23 Jul. 2015 from https://www.boundless.com/calculus/textbooks/boundlesscalculustextbook/inversefunctionsandadvancedintegration3/inversefunctionsexponentiallogarithmicandtrigonometricfunctions13/basesotherthaneandtheirapplications872803/