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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 - 1880 - 318 páginas
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A Treatise on Algebra

Elias Loomis - 1881 - 384 páginas
...number by the exponent of the power; the product is the logarithm of the required power. 399. TJie logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. If we extract the rth root of both members of Eq. (1),...
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A Practical Arithmetic

George Albert Wentworth, Thomas Hill - 1881 - 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* = i of log 2 = £ x 0.3010 = 0.0753. log .002* =...
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Elements of Algebra

George Albert Wentworth - 1881 - 380 páginas
...simply exponents (§ 294), therefore, when roots are expressed by fractional indices, 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* = \ oflog 2 = \ x 0.3010 = 0.0753. log .002* = }...
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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. KULE. Add...
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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". Hence log s = logp"...
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Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - 1882 - 104 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. RULE. Add...
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The Franklin Elementary Algebra

Edwin Pliny Seaver, George Augustus Walton - 1881 - 297 páginas
...root, i/N= b", whence it appears (Art. 384) that is the logarithm of y/jV. Hence The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. 395. Briefly expressed in formulas the propositions just proved are as follows: (1) }og(NN'N" . . .)...
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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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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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