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Bøker Bok 1120 av 49Ios- y" &cFrom which it is evident, that the logarithm of the product of any number...
" 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... "
An Introduction to Algebra: With Notes and Observations : Designed for the ... - Side 187
av John Bonnycastle - 1818 - 260 sider
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Elements of algebra

William Foster - 1840
...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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The principles of arithmetic. [Followed by] The principles of algebra

Wales Christopher Hotson - 1842
...properties of the indices of the same base. Hence, (1) In any system, the logarithm of a product, consisting of any number of factors, is equal to the sum of the logarithms of those factors. For, if a be the base of the system, and x, x', x", &c , the logarithms of n, n', n", &c., we have,...
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A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the ...

George Roberts Perkins - 1842 - 360 sider
...quantities is equal to the sum of the logarithms. And in general, the logarithm of a number consisting of any number of factors is equal to the sum of the logarithms of all its factors. (217.) It also follows from the above, that n times the logarithm of any number is...
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A Treatise on Algebra

Elias Loomis - 1846 - 346 sider
...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...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - 1846 - 503 sider
...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...
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A Treatise on Algebra

Elias Loomis - 1846 - 346 sider
...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...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - 1846 - 503 sider
...definition, r+x' is the logarithm of NN' ; that is to say, The logaritJim of the pro duct of two or more factors is equal to the sum of the logarithms of those factors. II. Divide equation (1) by (2). .•. by definition, x — z7 is the logarithm of ^ ; that is to say,...
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Elements of Algebra: Including Sturms' Theorem

Charles Davies - 1847 - 368 sider
...quantities themselves are equal : hence, y abc . . . . = ya X y SX ус . . . that is, íAe nth root of the product of any number of factors, is equal to the product of their nth roots. 1. Let us apply the above principle in reducing to its sim plest form the...
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The elements of algebra, with additions by W. Galbraith and W. Rutherford

John Bonnycastle - 1848
...the equation ; hence the logarithm of a negative number is imaginary. Properties of Logarithms. (1) The logarithm of the product of any number of factors...equal to the sum of the logarithms of those factors. Let p, Q, к, s be any quantities, and x, у, z, v their logarithms to any base a ; then if = P, a'...
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HIGHER ARITHMETIC

GEORGE R. PERKINS A.M., - 1849
...square root of 365, we decompose 365 into the prime factors 5 and 73, Now, it is obvious that the root of the product of any number of factors is equal to the product of their roots, hence, fhe square root of 365 is equal to the square root of 5 x 73, which...
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