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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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Manual of Mathematicall Tables

Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
...from which the rules for using logarithmic tables in numerical computations are derived. PROPOSITION I. t'he logarithm of the product of two numbers is equal to the sum of e logarithms of the numbers. If the numbers be N and M, let n = log N, and m = log Л/ to any ise a,...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - 1860 - 400 páginas
...since a is the base of the system, we have from the definition, 3/ + x" = log (N' x N") ; that is, The logarithm of the product of two numbers is equal to the tum of their logarithms. 231 • If we divide equation (1) by equation (2), member by member, we have,...
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Elementary Trigonometry: With a Collection of Examples

Thomas Percy Hudson - 1862 - 184 páginas
...is called the logarithm of N with reference to a, or, as it is usually expressed, to the base a. 2. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. Let a be the base, M, N the numbers, and x and y their logarithms respectively to the base a. Then...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - 1863 - 420 páginas
...unity. For, let a* = a; then x = log. a. But by (88), if a' = a, then x = 1, or log. a = 1. 3. — The 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. от, z = log. n. But by multiplication we have...
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Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 páginas
...y1 + log y", &c. = log (y + tf + f, &c.) (2) Therefore, the logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers forming the product. 10. If we divide two of the equations (1), member by member, we have a1~* = y-:...
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Elements of Surveying and Levelling: With Descriptions of the Instruments ...

Charles Davies - 1871 - 431 páginas
...(5), member by member, we have, 10" +q = mn; whence, by the definition, p + q = log (mn) (6.) That is, the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. 6. Dividing (4) by (5), member by member, we have, whence, by the definition, 10*- = -; n P ~ 9 = That...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1871 - 187 páginas
...we have, 10 = mn ; whence, by the definition, x + y = log (mn) (6.) That is, the logarithm of tJie product of two numbers is equal to the sum of the logarithms of the numbers. 6. Dividing ( 4 ) by ( 5 ), member by member, we have, whence, by the definition, «-y = "*(£) ........
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Harvard Examination Papers

1873 - 164 páginas
...(0.00130106) 2 ; <aooi30106 j,; 2.7 X (0.00130106)"- Use arithmetical complements in dividing. 6. Prove that the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. 7. Find, by logarithms, the values of the following quantities (to six significant figures): ^(0.0126534);...
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Surveying and Navigation: With a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1873 - 482 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. I! '(1) b• = m; then, by def., log m = a;. Let _ (2) b* = n; then, by def., log...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1864 - 490 páginas
...number corresponds to logarithm 3.63025? Am. .0042683. MULTIPLICATION BY LOGARITHMS. 13. Proposition. The logarithm of the product of two numbers is equal to the siim of their logarithms. C (1) b- = in; then, by def., log m=x. Let 1 (_ (2) b* = n; then, by def.,...
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