| John Bonnycastle - Algebra - 1813 - 460 pages
...itecessary information, of this kind, rnay be readily obtained. From which it is evident, that the logarithm **of the product of any number of factors is equal to the** sum of the logarithms of those factors. Hence, if all the factors of a given number, in any case of... | |
| Bewick Bridge - Algebra - 1818 - 254 pages
...nn'ri'ri", &c. =log. n -flog, n'+log. м'' + log. ra'" + &c. ; from which we infer that " the logarithm **of the product of any number of factors is equal to the** sum of their.logarithms." N a* 174. Again, _ = — =ax~*""; but the logarithm of a*-*"" n o."" N =x—x"";... | |
| John Bonnycastle - Algebra - 1818 - 328 pages
...&c. ; or los- yy'y" &c- =1°g- y+ i°s- y'+ Ios- y" &cFrom which it is evident, that the logarithm **of the product of any number of factors is equal to the** sum of the logarithms of those factors. Hence, if all the factors of a given number, in any case of... | |
| Bewick Bridge - Algebra - 1821 - 284 pages
...nriri.ri", &c. = log.re + log. я. + log. я" + log. re." + &c.; from which we infer that " the logarithm **of the product of any number of factors is equal " to the** sum of their logarithms." 174. Again, — = ~— a'-""; but the logarithm of a*-""" na N =x—x""\... | |
| William Galbraith - Astronomy - 1834 - 454 pages
...the logarithm of nx «' x n", &c.=log. n+log. w'+log. n", &c., from which we infer that the logarithm **of the product of any number of factors is equal to the** sum of their logarithms. N r* 11. Again — = -jr; but the logarithm of r*— *'=x — x' ; therefore,... | |
| John Charles Snowball - 1837 - 322 pages
...logarithms of a number in the two systems whose bases are a and e, is = — . lea 4. The logarithm **of the product of any number of factors is equal to the** sum of the logarithms of the several factors. For mnr.. = a1am.a1an.a1ar... But т.и.r... = a .-.... | |
| Bewick Bridge - Algebra - 1839 - 280 pages
...that the logarithm of nn'ri'ri", &c.=log. n+log. n' + log. n" + log. n'" + &c. ; ie "the logarithm **of the product of any number of factors is equal to the** sum of their logarithms." N at 181. Again, — =^7T1—a'^c"" ; but the logarithm of a*-*""— N x... | |
| Algebra - 1845 - 382 pages
...quantities themselves are equal : hence, y a6c . . . . = yaxy 6 Xyc.... that is, the nth roo£ «/" **the product of any number of factors, is equal to the product of their** nm roots. 1. Let us apply the above principle in reducing to its simplest form the imperfect power,... | |
| Charles William Hackley - Algebra - 1846 - 544 pages
...the following principle, which is merely an extension of that already proved in (Art. 51). The n"1 **root of the product of any number of factors is equal to the product of** the nrt roots oftlie different factors. Or, in algebraic language, Raise each of these expressions... | |
| Elias Loomis - Algebra - 1846 - 378 pages
...following principle, which is merely an extension of that already proved in the preceding Article. The nth **root of the product of any number of factors is equal to the product of** the nth roots of those factors. Or in algebraic language For raise each of these expressions to the... | |
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