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" The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. "
Elements of Geometry and Trigonometry from the Works of A.M. Legendre ... - Page 256
by Charles Davies - 1854 - 432 pages
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 319 pages
...equation (1) by equation (2), member by member, we have n -. M ,.-*•, 10 = — or, m — = log -=.: hence, The logarithm of the quotient of two numbers, is equal to tkt logarithm of the dividend diminished liy the logarithm of the divisor. Of Logarithme. 4. Sice...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1872 - 420 pages
...we have mn = a**" ; therefore, log. mn = x-\-z = log. m-)-log. n. 4. — The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm bf the divisor. For, let m = a*, n = a* ; then x = log. w, z = log. n. By division we have _ = a*-*...
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Elementary Algegra

Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...by the other, member by member, we have ax+'=mn, in which x+y is the logarithm of the product mn. 4. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. For, dividing the equation a? = m by the equation a" = n, member by member, we...
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Plane and spherical trigonometry. [With] Solutions of problems. [Followed by ...

Henry William Jeans - 1873
...the product : Thus, if x=ab, then log. a:=log. a + log. b (b) The logarithm of the quotient of any two numbers is equal to the logarithm of the dividend diminished by the logarithm of the divisor : Thus, if х=a-т-b, or -, then log. a;=log. a— log. b * For the proof of this general rule see...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 506 pages
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. (" (1) 6-= yn; then, by def., log TO = x. Let ] ( (2) 6 l = n;...
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Harvard Examination Papers

1873 - 164 pages
...(to six significant figures): (0x26534)^ V/(0.0357635) III. 1. Prove that the logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 2. Find, by logarithms, the values of the following quan*-• 3. Prove the formula (sin Af -f- (cos...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 276 pages
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Г (1) b" = m; then, by def., log m = x. Let i. (_ (2) b * —...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...those numbers. Also, since powers of the same quantity are divided by subtracting their exponents, the logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. Since the logarithm of 10 is 1, if a number be multiplied or divided.by 10, its...
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Elementary Trigonometry

James Hamblin Smith - Trigonometry - 1877 - 228 pages
...of logarithms to the particular base 10, we may omit the suffix. 148. Tlie logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m=a*, and n=as. Then - = a-, •'• s. - = xy = Ioga m- log. i. Thus tho operation of Division...
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Practical Treatise on the Differential and Integral Calculus: With Some of ...

William Guy Peck - Calculus - 1877 - 208 pages
...function of x, S and we have, after reduction, fs + ds\ ,,/iZs ds* ds3 . But the logarithm of a quotient, is equal to the logarithm of the dividend, diminished by the logarithm of the divisor; changing the form of the first member and suppressing all the terms in the second member, after the...
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