| Simon Newcomb - Logarithms - 1882 - 204 pages
...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... | |
| Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...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" . . .)... | |
| Stephen Roper - Mechanical engineering - 1884 - 740 pages
...use. Any power of a given number may be found by logarithms as follows : The logarithm of any power **of a given number is equal to the logarithm of the number** multiplied by the exponent of the power. Example.— To find the fifth power of 9, logarithm 9 = 0'954243... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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... | |
| Stephen Roper - Mechanical engineering - 1888 - 702 pages
...59049. Conversely. 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 -r- 3 = 1-204120, and the number... | |
| Edward Albert Bowser - Algebra - 1888 - 868 pages
...m" = (a1)" = a** ; whence by definition, log mp = px = p log m. (7) The logarithm of any root of a **number is equal to the 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')... | |
| Charles Ambrose Van Velzer, Charles Sumner Slichter - Algebra - 1888 - 234 pages
...by definition, \og,,nf=pr That is, logan>=p log,,«. (c) 10. THEOREM. The logarithm of any root of a **number is equal to the 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,... | |
| Edward Brooks - Algebra - 1888 - 344 pages
...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 *_!**;... | |
| Charles Davies - Algebra - 1889 - 330 pages
...r, we have, Whence, by definition, * = Log ym . . . . (S.) 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 applications of the above principles require a table of logarithms. A TABLK OF LOGARITHMS, is a... | |
| James Morford Taylor - Algebra - 1889 - 400 pages
...the number multiplied by the exponent of the power ; and the logarithm of any root of a number equals **the logarithm of the number divided by the index of the root.** 307. From the principles proved above, we see that by the use of logarithms the operations of multiplication... | |
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