| Benjamin Greenleaf - 1879
...to the power p, we have <ff = mp, in which xp = loga m f. 361 • The logarithm of the root of any **number is equal to the logarithm of the number, divided by the** index of the root. For, assume the equation, c?= m, and extracting the rth root of both members, we... | |
| Benjamin Greenleaf - 1879 - 309 páginas
...members to the power p, we have ax" = mP, in which xp = logn m p. 361. The logarithm of the root of any **number is equal to the logarithm of the number, divided by the** index of the root. For, assume the equation, ax = m, and extracting the rth root of both members, we... | |
| Elias Loomis - 1879 - 384 páginas
...the exponent "of the power ; the product is the logarithm of the required power. 399. The loganlhm **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),... | |
| William Findlay Shunk - 1880 - 318 páginas
...power of a number is equal to the logarithm of the number multiplied by the exponent of the power. **The logarithm of any root of a number is equal to the logarithm of the number divided by the** index of the root. 0. The preceding principles enable us to abridge labor in arithmetical calculations,... | |
| Stephen Roper - 1880 - 63 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. Hyperbolic logarithms is a system of logarithms, so called, because the numbers... | |
| 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),... | |
| 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* = }... | |
| 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* =... | |
| 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:... | |
| 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.... | |
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