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" The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. "
National Society's Monthly Paper - Página 55
1855
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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...
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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,...
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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 n = y. (1)X(2) =...
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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...
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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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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, •*-•-:•...
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 184 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 n = y. (1)X(2) = (3)...
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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...
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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,...
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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!...
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