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" The logarithm of a product is equal to the sum of the logarithms of its factors. "
The Elements of Algebra Preliminary to the Differential Calculus: And Fit ... - Page 223
by Augustus De Morgan - 1837 - 248 pages
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A treatise on fluxions: in two volumes

Colin MacLaurin - Calculus - 1801
...art. 728) +-+- + &c. This likewise follows from the property of logarithms, that the logarithm of the product is equal to the sum of the logarithms of the factors; and consequently the fluxion of the logarithm ofp equal to the sum <>f the fluxions of the logarithms...
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Elements of algebra, compiled from Garnier's French translation of L. Euler ...

Charles Tayler, Leonhard Euler - 1824
...shall resume pur former equation, viz. log. be = log. b + log. c, which comprehends the property that the logarithm of a product is equal to the sum of the logarithms of the factors. First, as log. 2 = x, and log. 10 = 1, we have log. 20 = ^+1 log. 200 = ^ + 2 log. 2000 = ^+3 log....
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Elements of algebra

William Smyth - Algebra - 1830 - 264 pages
...by member, we have yy' y" = a*+x'+x" whence. log y y'y"=* + x' + x"= log y + log y'+ logy" That is, the logarithm of a product is equal to the sum of the logarithms of the factors of this product. If then a multiplication be proposed, we take from a table of logarithms the logarithms...
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Elements of Algebra: Tr. from the French of M. Bourdon, for the ..., Volume 1

M. Bourdon (Louis Pierre Marie) - Algebra - 1831 - 389 pages
...the rule for the exponents (No. 180), we find yyy"y"' .... ^a'+*+J"+»"+' • • • Hence thai is, the logarithm of a product is equal to the sum of the logarithms of the factors of this product. Secondly. Suppose it is required to divide y by y', and let x and x' represent their...
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Elements of Algebra

William Smyth - Algebra - 1836 - 280 pages
...= a^ + *' + «" whence log y y' y" ~= x -\- x' -f x" = log y -f~ log y' -\- log y' . That is, //i« logarithm of a product is equal to the sum of the logarithms of llie factors of this product. If then a mulplication be proposed, we take from a table of logarithms...
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Elements of algebra priliminary to the differential calculus ...

Augustus De Morgan - Algebra - 1837 - 256 pages
...has its Logarithm between 0 and 1 1 and 2 2 and 3 Sec. 0 and —1 — 1 and —2 — 2 and —3 &c. THEOREM V. The logarithm of a product is equal to...logarithms of the factors. Let a be the base, and p, q, and r, the logarithms of P, Q, and K. Then P = a" Q = a" R = a' PQR = af+2+'• or log(PQR) =p...
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Treatise on the elements of algebra

James Bryce - 1837
...known, its logarithm in another system may be found. 192. Schol. i. It follows, from Art. 35, 40, that the logarithm of a product is equal to the sum of the logarithms of its factors; and that the logarithm of a quotient is equal to the difference of the logarithms of the...
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A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms ...

John Hymers - Trigonometry - 1841 - 151 pages
...logep ; and as this process may be continued to any number of factor», we conclude, generally, that the logarithm of a product is equal to the sum of the logarithms of its factors. 8. The logarithm of a quotient is equal to the logarithm of the dividend diminished by...
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Elements of Arithmetic and Algebra: For the Use of the Royal Military College

William Scott - Algebra - 1844 - 500 pages
...logarithms of yy'.y" ...; -„ y~, V~respcctively; whence, as has been already proved (Art. 208 — 211), the logarithm of a product is equal to the sum of the logarithms of the factors of that product ; the logarithm of a quotient is equal to the excess of the logarithm of the dividend...
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An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - Algebra - 1845 - 294 pages
...a1 =n, ax'=n', ax+x'=nXn'. The product, nXn' has for its logarithm x-\-x'; or, the logarithm of any product is equal to the sum of the logarithms of the factors of the product. In case we wished to multiply any two numbers by logarithms, search in the tables for...
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