 | Simon Newcomb - Logarithms - 1882 - 208 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 - 742 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 - 876 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 - 332 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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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
