 | John Bonnycastle - Algebra - 1813 - 456 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 - 326 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... | |
 | Charles Davies - 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,... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...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... | |
 | Charles William Hackley - Algebra - 1846 - 542 pages
...radicals of the second, third, or n rt degree, according to the index of the root required. The n a root of the product of any number of factors is equal to the product of the n rt roots of the different factors. Or, in algebraic language, = V« XV * X liaise each of these... | |
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The logarithm of the product of any number of factors is equal to the sum of the logarithms of the factors. 
