 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...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:... | |
 | Simon Newcomb - Logarithms - 1882 - 204 pages
...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.... | |
 | Simon Newcomb - Algebra - 1882 - 302 pages
...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".... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...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.... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 376 pages
...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... | |
 | George Albert Wentworth - 1883 - 536 pages
...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... | |
 | Henry Law - 1884 - 568 pages
...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... | |
 | Stephen Roper - Mechanical engineering - 1884 - 740 pages
...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,... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...root, 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... | |
 | Elias Loomis - Trigonometry - 1886 - 436 pages
...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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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
