 | Benjamin Peirce - 1855 - 308 pàgines
...in the above equation, it becomes log. p — n log. log. VP = ilZ; n that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. • The equation log. mm! = log. in -}- log. m', gives log. m'... | |
 | Joseph B. Mott - 1855 - 58 pàgines
...= n log a ; and if n = -, then log a m = - log a : mm r —r that is, the logarithm of any power or root of a number is equal to the logarithm of the number multiplied by the exponent ....... , ------ ----------- --------- (THEOREMS.) 1. log 81 = log 3 4 =... | |
 | William Smyth - 1856 - 264 pàgines
...1 "= IV"'; whence log. N m = — = x log. IV & w m That is, the logarithm of the root of any degree of a number is equal to the logarithm of the number divided by the index of the root. 123. The properties above are altogether independent of the base; we may take, therefore, as we have... | |
 | Benedict Sestini - 1857 - 258 pàgines
...- = ~x; - x 1 cc now x = lz; hence, 1.& or ?.j/z~= -lz; C that is, The logarithm of the root of any number is equal to the logarithm of the number divided by the degree or index of the root. From these theorems we infer, that when the logarithms of the numbers... | |
 | William Smyth - 1858 - 386 pàgines
...m = N"; whence log. JV™ = — = —'-—. tj mm That is, the logarithm of the root of any degree of a number is equal to the logarithm of the number divided by the index of the root. 125. The properties above are altogether independent of the base; we may take, therefore, as we have... | |
 | John Hymers - 1858 - 324 pàgines
...where r is any number whole or fractional, positive or negative. 10. The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. Since m = a x , m = Ja' = a ••• log,, (7™)=^ = -(log,, 11. Hence, if we have to multiply two... | |
 | Benjamin Peirce - 1858 - 296 pàgines
...n , or in the above equation, it becomes n log. p = n log. v' p, or n that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. The equation log. m m' = log. m -f- log. mi', gives log. m' =... | |
 | Charles Davies - 1860 - 332 pàgines
...denoted by r, we have, Whence, by definition, X - = Log <^m . . . . (8.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. The applications of the above principles require a table of logarithms. A TABLE OF LOGARITHMS, is a... | |
 | Benjamin Peirce - 1860 - 302 pàgines
...above equation, it becomes » log. p = n log. v/ p, log. ^ p = !£?-£; n that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. The equation log. m m' = log. m + log. m', gives log. m' = log.... | |
 | Henry Lee Scott - 1861 - 674 pàgines
...the product of the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. These properties of logarithms greatly facilitate arithmetical operations. For if multiplication is... | |
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the logarithm of the m th root of a number is equal to the logarithm of the number divided by the index of the root LOGARITHMS. 
