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" The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. "
Elementary Arithmetic: With Brief Notices of Its History - Page 10
by Robert Potts - 1876
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The Fluxional Calculus: An Elementary Treatise ...

Thomas Jephson - Calculus - 1826 - 472 pages
...\ / 'Va/ series. Hence /. 10 = '9 + -'- x ('9)2 4- fx ('9)3 + &c. = 2-302585093, c. 23. Vze logarithm of the product of two numbers is equal to the sum of their logarithms, and the logarithm of the quotient is equal to the difference of their logarithms....
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The elements of algebra

Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...2* = 16, ... in this system 2 = 14, 3 = 18, 4 = 116. . GENERAI, PROPERTIES OF LOGARITHMS. (501.) 1 The logarithm of the product of two numbers is equal to the sum of the logarithms of these numbers.1 For let aх = y, and aх, .= y', then for the base a, x = ly, and x' = ly. And aх...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...cases, which form the first four propositions of his Second Book. The first of them is as follows : The product of two numbers is equal to the sum of the products of one of them multiplied by the parts of the other. Thus, if 5 and 10 be the two numbers,...
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Manual of plane trigonometry, by J.A. Galbraith and S. Haughton

Joseph Allen Galbraith - 1852 - 84 pages
...10m. If we multiply these, NX M= 1o**™; therefore, log NX M—n + m = log N + log if. PROPOSITION I. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. If we divide the former of these equations by the latter N__ therefore N log -=n-ra = logAT-log M....
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Calendar of the University of Sydney

University of Sydney - 1853 - 810 pages
...or (J) a lava ; or (<•) hypabyssal ; or (rf) plutonic ? MATHEMATICS I. FIRST PAPER. 1. Explain why the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. Find 1 he cube root of 1002-5 and the fifth power of 1-025, using your tables, and compare...
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The practice and theory of arithmetic

William Frederick Greenfield - 1853 - 228 pages
...the sum of the products of each part of the multiplicand and multiplier 127 PKOP. 8.— To prove that the product of two numbers is equal to the sum of the products of the multiplicand by each part, of the multiplier . 127 PROP. 9. — To prove the Rule for...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...LOGARITHMIC ARITHMETIC. (Two Hours allowed for this Paper,) Section 1. 1. Define a logarithm; and show that the logarithm of the product of two numbers is equal to the sum of their logarithms ; and the logarithm of their quotient, to the difference of their logarithms. 2. Show...
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National Society's Monthly Paper

1855 - 264 pages
...annual motion of the Earth. LOGARITHMIC ARITHMETIc. SECT. I.— 1. Define a logarithm; and show that the logarithm of the product of two numbers is equal to the sum of their logarithms, and the logarithm of their quotient to the difference of their logarithms. 2. Show...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1857 - 408 pages
...since a is the base of the system, we have from the definition, x' + x" = log (Nt x N") ; that is, The logarithm of the product of two numbers is .equal to the turn of their logarithms. 231. If we divide equation (1) by equation (2), member by member, we have,...
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The Common-school Arithmetic: a Practical Treatise on the Science of Numbers

Dana Pond Colburn - 1858 - 288 pages
...8427 29. .0049 80. 73648 31. 4957.3 X 300. 32. 2796 X 8000. 50* Multiplication by Large Numbers. (a.) The product of two numbers is equal to the sum of the products obtained by multiplying one of them by the parta into which the other may be divided. (See...
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