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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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Logarithmic and Other Mathematical Tables: With Examples of Their Use and ...

Simon Newcomb - 1882 - 184 páginas
...equal to the logarithm of the number multiplied by the exponent of the power. IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. We thus derive the following rules: To find the product of several factors by logarithms....
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A School Algebra

Simon Newcomb - 1882 - 279 páginas
...the иth power, 10"* = p". Whence nh — log jo", or n log p = logy. THEOREM X. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Proof. Let s be the number, and let p be its nth root, so that p = VU and s = p"....
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A Practical Arithmetic

George Albert Wentworth, Thomas Hill - 1882 - 351 páginas
...11 x 0.4771 = 5.2481. 413. As logarithms are simply exponents, therefore (§381), The logarithm of a root of a number is equal to the logarithm of the number multiplied by the index of the root. Thus, log 2* = J of log 2 = } x 0.3010 = 0.0753. log .002* = J...
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Elements of Algebra

George Albert Wentworth - 1883
...be the logarithm of m. Then т = а*, and mr = (a*yr = af. .-. log mP = px, IV. The logarithm of the root of a number is equal to the logarithm of the number divided by thе index of the root. For, let x be the logarithm of m. Then m = of, and m = (aff = cff. 319. An...
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Mathematical tables for trigonometrical, astronomical, and nautical ...

Henry Law - 1884
...or, the logarithm of the nthpowerof m, is equal to n times the logarithm 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 = logj, m, then m = 6X ; let the square root...
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The Engineer's Handy-book: Containing a Full Explanation of the Steam-engine ...

Stephen Roper - 1884 - 675 páginas
...Any root of any number may be found by logarithms as follows: The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. Example. — To find the cube root of 4096, logarithm 4096 = 3-612360 -f- 3 = 1-204120,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1885 - 512 páginas
...indicated by r, of both members of (4), we have whence, by the definition, - = log \?m. (9.) 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 preceding principles enable us to abbreviate the operations of multiplication...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1886 - 199 páginas
...Required the seventh power of 0.8952. В EVOLUTION BY LOGARITHMS. 15. It is proved in Algebra, Art. 399, that the logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. Hence, to extract the root of a number by logarithms,...
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College Algebra: For the Use of Academies, Colleges, and Scientific Schools ...

Edward Albert Bowser - 1888 - 540 páginas
...log m ; then m = a*. Therefore m" = (a1)" = a** ; whence by definition, log mp = px = p log m. (7) The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For let x = log m ; then m = a1. 1 1 X Therefore m? = (a*)~r = ar ; whence by definition,...
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A Course in Algebra: Being Course One in Mathematics in the ..., Parte 1

Charles Ambrose Van Velzer, Charles Sumner Slichter - 1888 - 216 páginas
...Consequently nf=af*. Therefore, by definition, \og,,nf=pr That is, logan>=p log,,«. (c) 10. THEOREM. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let n be any number, and let loga n—x. Then, by definition, n=a* . Consequently...
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