 | 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 of N". n It is... | |
 | 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, as we have before... | |
 | 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; whole number answering... | |
 | William Lilly, Zadkiel - Astrology - 1852 - 584 pages
...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... | |
 | 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; whole_ number... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...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.... | |
 | Joseph B. Mott - Algebra - 1855 - 58 pages
...n log a ; T —Y and if n = -, then losam = - losa : m ° m 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 34 =... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...-(N')~n- *JW - - (6). But from the definition, yj — — log ( n-/N') ; 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. 234i From the principles demonstrated in the four preceding • articles, we deduce the following practical... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
..._. 10" =M~a' ± in which - is the 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 5th power of 9? Log 9 = 0.954243 ; 0.954243 X 5 = 4.771215; whole number answering... | |
 | John Hymers - Logarithms - 1858 - 324 pages
...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", .: log„ (Jm) = ^ = — (log.«»). 11. Hence, if we have to multiply two numbers together,... | |
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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. 
