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" The nth root of the product of any number of factors is equal to the product of the nth roots of those factors. "
A Treatise on Algebra - Page 138
by Elias Loomis - 1846 - 346 pages
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A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volume 1

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...
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An Elementary Treatise on Algebra

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"";...
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An Introduction to Algebra: With Notes and Observations : Designed for the ...

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...
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A Treatise on the Elements of Algebra

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""\...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

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,...
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The elements of plane trigonometry

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 .-....
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A Treatise on the Elements of Algebra

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...
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Elements of Algebra: Including Sturms' Theorem

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...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...SSaVy2 to its most simple form. 7. Reduce V 45a26Vd to its most simple form. 8. Reduce V 864a265c11 to its most simple form. (158.) Surds of any degree...and we obtain the same result. Thus the nth power of nV ab is ab. And the nth power of nv/ a X "-/ 6 is ("\/ a )" X (-V 6)» = ab. Hence, since the same...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 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 to the...
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