 | Adrien Marie Legendre - 1874 - 500 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... | |
 | William Guy Peck - 1875 - 348 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... | |
 | Horatio Nelson Robinson - 1875 - 430 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'+'... | |
 | Aaron Schuyler - 1875 - 284 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... | |
 | Robert Potts - 1876 - 392 páginas
.... «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 Potts - 1876 - 389 páginas
...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 +... | |
 | Robert Fowler Leighton - 1877 - 372 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... | |
 | University of Oxford - 1879 - 414 páginas
...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°... | |
 | William Findlay Shunk - 1880 - 362 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.... | |
 | George Albert Wentworth - 1881 - 406 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,... | |
| |
The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. 
