| 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). , „... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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'... | |
| 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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