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" The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. "
Manual of mathematical tables, by J.A. Galbraith and S. Haughton - Página viii
por Joseph Allen Galbraith - 1860
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 455 páginas
...member by member, we have, 10* + » = mn; whence, by the definition, x + y = log(mw) (6.) That is, the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. 8. Dividing ( 4 ) by ( 5 ), member by member, we have, •*-•-:• whence, by the definition, xy...
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Manual of Algebra

William Guy Peck - 1875 - 331 páginas
...ax+v _ mn. whence, from the definition, .x + у = Log mn; ... (5) hence, the following principle: 1°. The logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. If we divide (3) by (4), member by member, we have, n whence, from the definition, xy...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - 1875 - 412 páginas
...unity. For, let a' = a ; then x = log. a. But by 88, if a' = a, then x = 1, or log. a = 1. 3. TJie logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. For, let m = a', n = a' ; then x = log. m, z = log. n. But by multiplication, mn = a'+'...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 251 páginas
...number corresponds to logarithm 3.63025? Ans. .0042683. MULTIPLICATION BY LOGARITHMS. 13. Proposition. The logarithm of the product of two numbers is equal to the sum of their logarithms. С (1) b" = m; then, by def., log m = x. Let \ (_ (2) b* = n; then, by def., log...
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Elementary Arithmetic: With Brief Notices of Its History, Volúmenes1-12

Robert Potts - 1876
.... «l = <lloS««l . elogaK2 = alog«!ll +loSo«í And log„{M, . %} =log„«, + logA by def. Or, the logarithm of the product of two numbers, is equal to the sum of the logarithms of the numbers themselves. COR. In a similar way it may be shewn that the logj«, . «, . «s . : . . } =log„«i...
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ELEMENTARY ARITHMETIC, WITH BRIEF NOTICES OF ITS HISTORY

ROBERT POTTS - 1876
...a l °s« u i . a l °S" u 2 — ^osa«^ logora And log^i . u. 2 ] ^log^! + Iog ß w 2 by def. Or, the logarithm of the product o f two numbers, is equal to the -sum of the logarithms of the numbers themselves. COR. In a similar way it may be shewn that the log a {w! . w a . w a . : . . } =logA +...
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 343 páginas
...ол-i nc>2 TT (0.00130106)2; 2; ' Use (000130106) arithmetical complements in dividing. 6. Prove that the logarithm of the product of two numbers is equal to the sxim of the logarithms of the numbers. 7. Find, by logarithms, the values of the following quantities...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...of a right-angled triangle, in which the perpendicular is 127 and the hypotenuse 325. 9. Prove that the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers themselves. Find A, when 10 tan^ = 7 sin 15° 30'. 10. In the triangle ABC, if B = 57° 45', C = 105°...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - 1880 - 318 páginas
...lies between 10 and 100; hence its logarithm lies between 1 and 2, as docs the logarithm of 74. 5. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor....
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Elements of Algebra

George Albert Wentworth - 1881 - 380 páginas
...following general proofs to the base a should be noticed. I. The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm,...
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