 | Aaron Schuyler - Navigation - 1873 - 536 pages
...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... | |
 | Aaron Schuyler - Measurement - 1864 - 506 pages
...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.,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...and (5), 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,... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...mn; whence, from the definition, x + y — Log mn ; . . . (5) hence, the following principle : 1°. The logarithm of the product of two numbers is equal...numbers. If we divide (3) by (4), member by member, we have, whence, from the definition, x — y — Log ^; . . . . (6) hence, the following principle: 2°.... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...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'+' ; therefore,... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...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... | |
 | Robert Potts - Arithmetic - 1876 - 418 pages
...11.2 — «log'«l . iZloga'3 = (Z1og'«l +'o'a«3 And loga{«, . «,} = loga«, + logau, 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 Iog0{«, . «3 . «3 . : . . } =log^/,... | |
 | Robert Potts - Arithmetic - 1876 - 392 pages
.... «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... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...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... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...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',... | |
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The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. 
