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The logarithm function remains a staple of mathematical analysis, but printed tables of logarithms gradually diminished in importance in the twentieth century as mechanical calculators and, later, electronic pocket calculators and computers took over computations that required high accuracy. [54]
The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. [1]
The logarithm function became a staple of mathematical analysis, but printed tables of logarithms gradually diminished in importance in the twentieth century as multiplying mechanical calculators and, later, electronic computers took over high accuracy computation needs. [10]
Tables of logarithms need only include the mantissa, as the characteristic can be easily determined by counting digits from the decimal point. [31] The characteristic of 10 · x is one plus the characteristic of x, and their mantissas are the same. Thus using a three-digit log table, the logarithm of 3542 is approximated by
An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [b] Thus, log tables need only show the fractional part. Tables of common logarithms ...
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x"). An equivalent and more succinct definition is that the function f : x → l o g b x {\displaystyle f\colon x\to log_{b}x} is the inverse function to the function f : x → b x . {\displaystyle ...
A logarithmic timeline is a timeline laid out according to a logarithmic scale. This necessarily implies a zero point and an infinity point, neither of which can be displayed. The most natural zero point is the Big Bang, looking forward, but the most common is the ever-changing present, looking backward. (Also possible is a zero point in the ...
Common logarithm; Complex logarithm; Discrete logarithm. Discrete logarithm records; e. Representations of e; El Gamal discrete log cryptosystem; Harmonic series; History of logarithms; Hyperbolic sector; Iterated logarithm; Otis King; Law of the iterated logarithm; Linear form in logarithms; Linearithmic; List of integrals of logarithmic ...