| George Albert Wentworth - 1881 - 406 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* = }... | |
| Simon Newcomb - 1882 - 204 páginas
...called functions of the argument, and are found in the same columns or lines as the argument, but ih the body of the table. In a table. of logarithms the...find the product of several factors by logarithms. KULE. Add the logarithms of the several factors. Enter the table with the sum as а пеги logarithm,... | |
| Simon Newcomb - 1882 - 302 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"... | |
| Edwin Pliny Seaver, George Augustus Walton - 1881 - 304 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" . . .)... | |
| John Bascombe Lock - 1882 - 378 páginas
...the power of a number is equal to the product of the logarithm of the number by the index denoting the power. (iv) The logarithm of the root of a number is equal to the result of dividing the logarithm of the number by the number denoting the root. Let m and n be any... | |
| George Albert Wentworth, Thomas Hill - 1882 - 376 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... | |
| George Albert Wentworth - 1883 - 536 páginas
...of the power. For, let x 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... | |
| Stephen Roper - 1884 - 740 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... | |
| Charles Davies, Adrien Marie Legendre - 1885 - 538 páginas
...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 and division, by... | |
| John Bascombe Lock - 1885 - 368 páginas
...the power of a number is equal to the product of the logarithm of the number by the index denoting the power. (iv) The logarithm of the root of a number is equal to the result of dividing the logarithm of the number by the number denoting the root. Let m and n be any... | |
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