 | John Bonnycastle - Algebra - 1813 - 456 pages
...every 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...equal to the sum of the logarithms of those factors. Hence, if all the factors of a given number, in any case of this kind, be supposed equal to each other,... | |
 | John Bonnycastle - Algebra - 1818 - 326 pages
...&c=log. yy'y" &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...equal to the sum of the logarithms of those factors. Hence, if all the factors of a given number, in any case of this kind, be supposed equal to each other,... | |
 | Bewick Bridge - Algebra - 1818 - 254 pages
...logarithm of 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"";... | |
 | Bewick Bridge - Algebra - 1821 - 648 pages
...logarithm of nn'n"ri", &c. = log.n •flog, n' + log. w" + 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—f'"; but the logarithm of a*—"" na* =xx""; .'. the logarithm... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...of this kind may 6e readily obtained. From which it is evident, that the logarithm of the pro-- duct 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 this kind, be supposed equal to each other,... | |
 | William Galbraith - Astronomy - 1834 - 454 pages
...shown that 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, N the... | |
 | John Charles Snowball - 1837 - 322 pages
...connecting the 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 .-. \a(mnr..) = \am + }an + }ar... | |
 | Charles William Hackley - Trigonometry - 1838 - 328 pages
...a similar manner a »+''+'" = nrin" and so on. Or in general the logarithm of a product of several factors is equal to the sum of the logarithms of those factors seperately. * As the number 3905073 is too large to be found in the tables, the method of finding its... | |
 | Bewick Bridge - Algebra - 1839 - 280 pages
...might be shown 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 — -x"";... | |
 | William Foster - 1840 - 92 pages
...and I, 2 &c. if it be only a decimal with 3, 4, &c. places. 6. The logarithm of a product consisting of any number of factors, is equal to the sum of the logarithms of those factors. Let a be the base : .r, x', x" &c. the logarithms of y, y', y" &c , then we have (by Def. 2). , „... | |
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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. 
