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" ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. "
New Plane and Spherical Trigonometry - Pągina 44
per Webster Wells - 1896 - 126 pągines
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The elements of algebra, with additions by W. Galbraith and W. Rutherford

John Bonnycastle - 1848 - 334 pągines
...PQKS = cf. af . a' . a" = a"+'+„ + „; hence log.PQBS = (2) The logarithm of a fractional quantity is equal to the logarithm of the numerator minus the logarithm of the denominator. Let a" = P and a* = Q, then x = }ogje and y = log.Q ; hence Q ~ u-- - ' .-. log,- — xy — log.P—...
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Bonnycastle's Introduction to Algebra: Containing the Indeterminate and ...

John Bonnycastle - 1851 - 288 pągines
...Hence, the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus the logarithm of the denominator. And if each member of the common equation a? — y be raised to the fractional power denoted by —...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - 1852 - 408 pągines
...divisor, is equal to the logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction is equal to the logarithm...numerator, minus the logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms, the operation of Multiplication...
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A Treatise on Algebra

Elias Loomis - 1855 - 356 pągines
...&c. log. 160 =4a;+1, log. 16000 = log. 1600=4a;+2, log. 160000=, &c. We have seen, in Art. 339, that the logarithm of a fraction is equal to the logarithm...numerator minus the logarithm of the denominator. Hence, log. 5= log. (y) = l— a;. Hence.log. 50 =2— x, log. 5000 = log. 500 =3- x, log. 50000 =,...
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Mathematical Key: New Combinations in Respect to the Binomial Theorem and ...

Joseph B. Mott - 1855 - 58 pągines
...; aa but from equation (1), log 6 = log^ — loga; therefore, log 2 = log p — log a : a that is, the logarithm of a fraction is equal to the logarithm...numerator, minus the logarithm of the denominator. (THEOREM 2.) Or, for a more general theorem for fractions, let us resume the equation log ^ — log...
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Treatise on Algebra, for the Use of Schools and Colleges

William Smyth - 1855 - 370 pągines
...therefore by adding the logarithm of 5 to that of 7. Since moreover the logarithm of a fraction will be equal to the logarithm of the numerator minus the logarithm of the denominator, it will be sufficient to place in the tables the logarithms of entire numbers. 201. Below we have a...
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A Treatise on Algebra

Benedict Sestini - 1857 - 258 pągines
...or a*-* = - ; a* vv a" z z and consequently, x — y = I.-, that is, The logarithm of the quotient is equal to the logarithm of the numerator, minus the logarithm of the denominator. Raise to the exponent c both members of the equation a*= z, we will have (a 1 )' = z° or a" = z°,...
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A Treatise on Algebra: For the Use of Schools and Colleges

William Smyth - 1858 - 344 pągines
...therefore by adding the logarithm of 5 to that of 7. Since moreover the logarithm of a fraction will be equal to the logarithm of the numerator minus the logarithm of the denominator, it will be sufficient to place in the tables the logarithms of entire numbers. 201. Below we have a...
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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1863 - 482 pągines
...logarithm of the quotient is equal to the logarithm of the dividend minus that of the divisor ; or the logarithm of a fraction is equal to the logarithm of the numerator made less by that of the denominator. 1 10. Farther, A A-" = — n A A. For A-" = — : therefore A...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - 1852 - 420 pągines
...divisor, is equal to the logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction is equal to the logarithm of the numerator minus (he logarithm of the denominator. From this article, and the preceding, we see that by means of logarithms,...
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