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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.
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 4
por William Findlay Shunk - 1890 - 339 páginas
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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, and the number...
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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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## 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...logarithm of the number divided by the. index of the root. The preceding principles enable us to abbreviate the operations of multiplication and division, by...
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## The Field Engineer: a Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - 1886 - 325 páginas
...and 2, as does the logarithm of 74. 5. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. The logarithm...subtraction instead of multiplication and division. П. MANNER OF USING THE TABLES. TO FIND THE LOGARITHM OF ANY NUMBER. 1. First find the characteristic...
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## Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1886 - 199 páginas
...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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## A Course in Algebra: Being Course One in Mathematics in the ..., Parte1

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...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 v/«=a?. Therefore,...
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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...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, 1 x 1 log(m')...
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## The Normal Elementary Algebra: Containing the First Priniples of the Science ...

Edward Brooks - 1888 - 336 páginas
...nth power, B"XIll = AT". Whence, log Jl/" = nxm. Or log M" = nx log if. PRIN. 6. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, let m = log M. Then, . B™ = M. Taking nth root, E* = M *. Whence, logJHA=-. 71 or k if *_!**;...
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## A High School Arithmetic (Wentworth & Hill's Practical Arithmetic)

George Albert Wentworth - 1888 - 362 páginas
...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* = Joflog2 = Jx0.3010 = 0.0753. log .002* = J of (7.3010...
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## University Algebra: Embracing a Logical Development of the Science with ...

Charles Davies - 1889 - 320 páginas
...both members of ( 3 ), denoted by r, we have, Whence, by definition, * = Log ym . . . . (S.) That is, the logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. The applications of the above principles require a table of logarithms. A TABLK OF LOGARITHMS, is a...
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