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" The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. log» MN = log» M + log "
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 2
por William Findlay Shunk - 1908 - 345 páginas
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The Common-school Arithmetic: a Practical Treatise on the Science of Numbers

Dana Pond Colburn - 1858 - 276 páginas
...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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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - 1859 - 306 páginas
...then and, by substituting these values in the last logarithmic equation, we have, considering that the logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor, log. (»+i>- log. B=2ar(^+^^+-pL—5.+fa,. ;)or log (w+1)= log....
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Manual of mathematical tables, by J.A. Galbraith and S. Haughton

Joseph Allen Galbraith - 1860
...which the rules for using logarithmic tal1ies in numerical computations are derived. PROPOSITI°N I. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. If the numbers be N and M, let n = log N, and m = log M to any base a, then by the definition, By multiplication,...
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Manual of Mathematicall Tables

Joseph Allen Galbraith, Samuel Haughton - 1860 - 252 páginas
...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 ...

T. 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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