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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. "
Encyclopaedia Perthensis; Or Universal Dictionary of the Arts, Sciences ... - Página 323
1816
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
....•. 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...
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A Treatise on Algebra

Elias Loomis - 1846 - 346 páginas
...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...
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A Treatise on Algebra

Elias Loomis - 1846 - 346 páginas
...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...
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - 1846 - 503 páginas
....-. 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...
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Elementary Algebra: For the Use of Schools

William Smyth - 1851 - 236 páginas
...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,...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
..._! 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;...
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Rudimentary Treatise on Logarithms

Henry Law - 1853 - 68 páginas
...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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 432 páginas
...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;...
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An Elementary Treatise on Algebra: To which are Added Exponential Ewquations ...

Benjamin Osgood Peirce - 1855 - 288 páginas
...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...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. m' = log. m TO' — log....
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1855 - 178 páginas
...Required the seventh power of 0.8952. EVOLUTION BY LoGARITHMS. (15.) It is proved in Algebra, Art. 341, that the logarithm of any root of a number is equal to the logarithm of that numoer divided by the index of the root. Hence, to extract the oot of a number by logarithms,...
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