Definition of Logarithm. Meaning of Logarithm. Synonyms of Logarithm

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Definition of Logarithm

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Antilogarithm
Antilogarithm An`ti*log"a*rithm, n. (Math.) The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.
Antilogarithmic
Antilogarithm An`ti*log"a*rithm, n. (Math.) The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. -- An`ti*log`a*rith"mic, a.
Arithmetical complement of a logarithm
Arithmetical Ar`ith*met"ic*al, a. Of or pertaining to arithmetic; according to the rules or method of arithmetic. Arithmetical complement of a logarithm. See Logarithm. Arithmetical mean. See Mean. Arithmetical progression. See Progression. Arithmetical proportion. See Proportion.
Binary logarithms
Binary Bi"na*ry, a. [L. binarius, fr. bini two by two, two at a time, fr. root of bis twice; akin to E. two: cf. F. binaire.] Compounded or consisting of two things or parts; characterized by two (things). Binary arithmetic, that in which numbers are expressed according to the binary scale, or in which two figures only, 0 and 1, are used, in lieu of ten; the cipher multiplying everything by two, as in common arithmetic by ten. Thus, 1 is one; 10 is two; 11 is three; 100 is four, etc. --Davies & Peck. Binary compound (Chem.), a compound of two elements, or of an element and a compound performing the function of an element, or of two compounds performing the function of elements. Binary logarithms, a system of logarithms devised by Euler for facilitating musical calculations, in which 1 is the logarithm of 2, instead of 10, as in the common logarithms, and the modulus 1.442695 instead of .43429448. Binary measure (Mus.), measure divisible by two or four; common time. Binary nomenclature (Nat. Hist.), nomenclature in which the names designate both genus and species. Binary scale (Arith.), a uniform scale of notation whose ratio is two. Binary star (Astron.), a double star whose members have a revolution round their common center of gravity. Binary theory (Chem.), the theory that all chemical compounds consist of two constituents of opposite and unlike qualities.
Hyperbolic logarithm
Hyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. 2. (Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.' --Fuller. Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. Hyperbolic logarithm. See Logarithm. Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.
Index of a logarithm
3. A table for facilitating reference to topics, names, and the like, in a book; -- usually alphabetical in arrangement, and printed at the end of the volume. 4. A prologue indicating what follows. [Obs.] --Shak. 5. (Anat.) The second digit, that next pollex, in the manus, or hand; the forefinger; index finger. 6. (Math.) The figure or letter which shows the power or root of a quantity; the exponent. [In this sense the plural is always indices.] Index error, the error in the reading of a mathematical instrument arising from the zero of the index not being in complete adjustment with that of the limb, or with its theoretically perfect position in the instrument; a correction to be applied to the instrument readings equal to the error of the zero adjustment. Index expurgatorius. [L.] See Index prohibitorius (below). Index finger. See Index, 5. Index glass, the mirror on the index of a quadrant, sextant, etc. Index hand, the pointer or hand of a clock, watch, or other registering machine; a hand that points to something. Index of a logarithm (Math.), the integral part of the logarithm, and always one less than the number of integral figures in the given number. It is also called the characteristic. Index of refraction, or Refractive index (Opt.), the number which expresses the ratio of the sine of the angle of incidence to the sine of the angle of refraction. Thus the index of refraction for sulphur is 2, because, when light passes out of air into sulphur, the sine of the angle of incidence is double the sine of the angle of refraction. Index plate, a graduated circular plate, or one with circular rows of holes differently spaced; used in machines for graduating circles, cutting gear teeth, etc. Index prohibitorius [L.], or Prohibitory index (R. C. Ch.), a catalogue of books which are forbidden by the church to be read; the index expurgatorius [L.], or expurgatory index, is a catalogue of books from which passages marked as against faith or morals must be removed before Catholics can read them. These catalogues are published with additions, from time to time, by the Congregation of the Index, composed of cardinals, theologians, etc., under the sanction of the pope. --Hook. Index rerum [L.], a tabulated and alphabetized notebook, for systematic preservation of items, quotations, etc.
Logarithmetic
Logarithmetic Log`a*rith*met"ic, Logarithmetical Log"a*rith*met"ic*al, a. See Logarithmic.
Logarithmetical
Logarithmetic Log`a*rith*met"ic, Logarithmetical Log"a*rith*met"ic*al, a. See Logarithmic.
Logarithmetically
Logarithmetically Log`a*rith*met"ic*al*ly, adv. Logarithmically.
Logarithmic
Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.
Logarithmic
Tangent Tan"gent, n. [L. tangens, -entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. Attain, Contaminate, Contingent, Entire, Tact, Taste, Tax, v. t.] (Geom.) A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See Trigonometrical function, under Function. Artificial, or Logarithmic, tangent, the logarithm of the natural tangent of an arc. Natural tangent, a decimal expressing the length of the tangent of an arc, the radius being reckoned unity. Tangent galvanometer (Elec.), a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current. Tangent of an angle, the natural tangent of the arc subtending or measuring the angle. Tangent of an arc, a right line, as ta, touching the arc of a circle at one extremity a, and terminated by a line ct, passing from the center through the other extremity o.
Logarithmic curve
Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.
Logarithmic spiral
Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.
Logarithmic spiral
Spiral Spi"ral, n. [Cf. F. spirale. See Spiral, a.] 1. (Geom.) A plane curve, not re["e]ntrant, described by a point, called the generatrix, moving along a straight line according to a mathematical law, while the line is revolving about a fixed point called the pole. Cf. Helix. 2. Anything which has a spiral form, as a spiral shell. Equiangular spiral,a plane curve which cuts all its generatrices at the same angle. Same as Logarithmic spiral, under Logarithmic. Spiral of Archimedes, a spiral the law of which is that the generatrix moves uniformly along the revolving line, which also moves uniformly.
Logarithmical
Logarithmic Log`a*rith"mic, Logarithmical Log`a*rith"mic*al, a. [Cf. F. logarithmique.] Of or pertaining to logarithms; consisting of logarithms. Logarithmic curve (Math.), a curve which, referred to a system of rectangular co["o]rdinate axes, is such that the ordinate of any point will be the logarithm of its abscissa. Logarithmic spiral, a spiral curve such that radii drawn from its pole or eye at equal angles with each other are in continual proportion. See Spiral.
Logarithmically
Logarithmically Log`a*rith"mic*al*ly, adv. By the use of logarithms.
logarithms
Logistic Lo*gis"tic, Logistical Lo*gis"tic*al, a. [Gr. ? skilled in calculating, ? to calculate, fr. lo`gos word, number, reckoning: cf. F. logistique.] 1. Logical. [Obs.] --Berkeley. 2. (Math.) Sexagesimal, or made on the scale of 60; as, logistic, or sexagesimal, arithmetic. Logistic, or Proportional, logarithms, certain logarithmic numbers used to shorten the calculation of the fourth term of a proportion of which one of the terms is a given constant quantity, commonly one hour, while the other terms are expressed in minutes and seconds; -- not now used.
Naperian logarithms
Napierian Na*pie"ri*an, Naperian Na*pe"ri*an,, a. Of, pertaining to, or discovered by, Napier, or Naper. Naperian logarithms. See under Logarithms.
Proportional logarithms
Proportional Pro*por"tion*al, a. [L. proportionalis: cf. F. proportionnel.] 1. Having a due proportion, or comparative relation; being in suitable proportion or degree; as, the parts of an edifice are proportional. --Milton. 2. Relating to, or securing, proportion. --Hutton. 3. (Math.) Constituting a proportion; having the same, or a constant, ratio; as, proportional quantities; momentum is proportional to quantity of matter. Proportional logarithms, logistic logarithms. See under Logistic. Proportional scale, a scale on which are marked parts proportional to the logarithms of the natural numbers; a logarithmic scale. Proportional scales, compasses, dividers, etc. (Draughting), instruments used in making copies of drawings, or drawings of objects, on an enlarged or reduced scale.
Proportionallogarithms
, those logarithms (devised by John Speidell, 1619) of which the base is 2.7182818; -- so called from Napier, the inventor of logarithms. Logistic or Proportionallogarithms., See under Logistic.

Meaning of Logarithm from wikipedia

- the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of...
- The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately...
- given real numbers a {\displaystyle a} and b {\displaystyle b} , the logarithm l o g b ( a ) {\displaystyle log_{b}(a)} is a number x {\displaystyle...
- constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after...
- the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian...
- In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus...
- In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which...
- binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the...
- iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to...
- The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and...