 | Elias Loomis - Algebra - 1846 - 380 pages
...shall obtain x 1 therefore, according to the definition, - is the logarithm of N" ; that is to say, . The logarithm of any root of a number, is equal to the logarithm of that number divided by the index of the root. EXAMPLES. Ex. 1. Find the square root of 81 by means... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...we shall obtain i therefore, according to the definition, - is the logarithm of N" ; that is to say, The logarithm of any root of a number, is equal to the logarithm of that number divided by the index of the root. EXAMPLES. Ex. 1. Find the square root of 81 by means... | |
 | Charles William Hackley - Algebra - 1846 - 544 pages
....-. by definition, - is the logarithm of N" ; that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the last two cases, we shall find mm* N»=a"% whence — is the logarithm... | |
 | Benjamin Peirce - Algebra - 1851 - 294 pages
...Corollary. If we substitute ™= \/P, in the above equation, it becomes • log. p = n log. v/ p, log. that is, the logarithm of any root of a number is...root. 13. Corollary. The equation log. mm, = log. m -f- log. m,, gives log. m' = log. mm' — log. m ; that is, the logarithm of one factor of a product... | |
 | William Smyth - Algebra - 1851 - 272 pages
...log.N am = N'n; whence log. Nm — — r= — — 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. The properties above are altogether independent of the base ; we may take, therefore,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
..._! 10n=ifn' i in which - ig ^e logarithm of M n : that is, n The logarithm of the root .of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the 5th power of 9? Log 9. =0.954243; 0.954243x5-4.771215;... | |
 | Henry Law - Logarithms - 1853 - 84 pages
...the logarithm of the nth root of m, is equal to n times the lugar rithm of m. PROPOSITION P. THEOREM. The logarithm of any root of a number, is equal to the logarithm of that number, divided by the exponent of the root. Let X = log;, m, then m = 6X ; let the square root... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...members, we have HI which - is tne logarithm of M" : that is, n The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the oth power of 9 ? Log 9 = 0.954243 ; 0.954243 X 5 = 4.771215;... | |
 | Benjamin Peirce - Algebra - 1855 - 296 pages
...Corollary. If we substitute in the above equation, it becomes n log. p = n log. v/ p, log. ^p=^Lf; that is, the logarithm of any root of a number is...log. mm! = log. m + log. m!, gives log. m! = log. m m' — log. m ; that is, the logarithm of one factor of a product is equal to the logarithm of the... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...If we substitute p — ran, in the above equation, it becomes log. p = n log. v/ p, log. v P = k*Z; n that is, the logarithm of any root of a number is...root. 13. Corollary. • The equation log. m m' = log. TO + l°g. n»'i gives log. m' = log. m TO' — log. TO ; that is, the logarithm of one factor of a... | |
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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
