 | Nathan Scholfield - 1845 - 894 sider
....•. by def. (2). — 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 two last cases, we shall find, •fjj T~ nk whence, — is the logarithm of N "»". 4... | |
 | Charles William Hackley - 1846 - 544 sider
....-. 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 of N". n It is... | |
 | Elias Loomis - 1846 - 380 sider
...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 - 1846 - 376 sider
...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... | |
 | William Smyth - 1851 - 272 sider
...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, as we have before... | |
 | Adrien Marie Legendre - 1852 - 436 sider
..._! 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; whole number answering... | |
 | William Lilly, Zadkiel - 1852 - 584 sider
...logarithm of the quotient. Also the logarithm multiplied by the index of the power raises the power ; and the logarithm of the number divided by the index of the root extracts the root, &c. Logarithms are a series of numbers in arithmetical progression, which answer... | |
 | Henry Law - 1853 - 84 sider
...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 - 1854 - 436 sider
...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; whole_ number... | |
 | Benjamin Peirce - 1855 - 308 sider
...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 equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. • The equation log. m m' = log. TO + l°g. n»'i gives log.... | |
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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. 
