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" 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. "
An Introduction to Algebra: With Notes and Observations : Designed for the ... - Side 201
av John Bonnycastle - 1818 - 260 sider
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A Treatise on Algebra, in Practice and Theory: With Notes and ..., Volum 1

John Bonnycastle - 1813 - 456 sider
...Borda, where every itecessary information, of this kind, rnay be readily obtained. From which it is evident, that the logarithm of the product of any...denoted by m, the preceding property will then become m log. ?/ = log. ym. From which it appears, that the logarithm of the wth power of any number is equal...
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An Elementary Treatise on Algebra

Bewick Bridge - 1818 - 254 sider
...the 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"";...
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A Treatise on the Elements of Algebra

Bewick Bridge - 1821 - 284 sider
...the logarithm of 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""\ .'. the...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - 1825 - 336 sider
...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...to each other, and the sum of them be denoted by. in, the preceding, property will then become log. yn=m log. y. From which it appears, that the logarithm...
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A Treatise on the Elements of Algebra

Bewick Bridge - 1828 - 260 sider
...shewn that the logarithm of n ra'я"ra'",&c. = log. я + log. ra' + log. ?i" + log. n" + &c. ; ie " the logarithm of the " product of any number of factors is equal to the sum of their " logarithms" 181. Again, — = -*m=.ax— *""; but the logarithm of a*-1"" =x— x""; .'.the...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - 1827 - 412 sider
...be shown that the logarithm of nx я' x n", &c.=log. n_(-log. n' + 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 r1 11. Again — =—¿¡ but the logarithm of r*-*=x — x' ; therefore, fb Т...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - 1834 - 454 sider
...might be 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...
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The elements of plane trigonometry

John Charles Snowball - 1837 - 322 sider
...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...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - 1838 - 328 sider
...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...
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A Treatise on the Elements of Algebra

Bewick Bridge - 1839 - 280 sider
...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"";...
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