 | 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... | |
 | Henry Law - 1884 - 568 páginas
...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... | |
 | Charles Davies, Adrien Marie Legendre - 1885 - 538 páginas
...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...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... | |
 | Elias Loomis - 1886 - 436 páginas
...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,... | |
 | Charles Ambrose Van Velzer, Charles Sumner Slichter - 1888 - 234 páginas
...Consequently nf=af*. Therefore, by definition, \og,,nf=pr That is, logan>=p log,,«. (c) 10. THEOREM. The logarithm of any root of a number is equal to...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 Albert Bowser - 1888 - 868 páginas
...log m ; then m = a*. Therefore m" = (a1)" = a** ; whence by definition, log mp = px = p log m. (7) The logarithm of any root of a number is equal to...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')... | |
 | Edward Brooks - 1888 - 344 páginas
...nth power, 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 *_!**;... | |
 | George Albert Wentworth - 1888 - 392 páginas
...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* = Joflog2 = Jx0.3010 = 0.0753. log .002* = J of (7.3010... | |
 | Charles Davies - 1889 - 330 páginas
...both members of ( 3 ), denoted by r, we have, Whence, by definition, * = Log ym . . . . (S.) That is, the logarithm of any root of a number is equal to...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 - 1889 - 400 páginas
...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. 
