...(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);...

...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...

...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.,...

...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...

...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...

...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'+'...

...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...

.... «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...

...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 +...

...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...