Bases Other than e and their Applications
Among all choices for the base
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 "$\text{ld}\, n$ " 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
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:
Thus,
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 baseten logarithms were given in appendices of many books. Such a table of "common logarithms" gave the logarithm—often to four or five decimal places—of each number in the lefthand column, which ran from
Because baseten logarithms were most useful for computations, engineers generally wrote
Binary logarithm (
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 "
Key Term Reference
 binary
 Appears in these related concepts: Logarithmic Functions, Gender as a Spectrum and Transgender Identities, and Sexual Orientation
 e
 Appears in these related concepts: Natural Logarithms, Business Stakeholders: Internal and External, and The Number e
 function
 Appears in these related concepts: Visualizing Domain and Range, The Vertical Line Test, and Solving Differential Equations
 inverse
 Appears in these related concepts: Inverse Functions, The Law of Universal Gravitation, and Hyperbolic Functions
 inverse function
 Appears in these related concepts: Introduction to Inverse Functions, Introduction to Exponential and Logarithmic Functions, and Inverse Trigonometric Functions
 natural logarithm
 Appears in these related concepts: The Integral Test and Estimates of Sums, Common Bases of Logarithms, and Converting between Exponential and Logarithmic Equations
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