 | Benjamin Greenleaf - 1879 - 322 pàgines
...to the power p, we have a* p = m", in which xp = log,, m r . 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, n x = m, and extracting the rth root of both members, we have, X n r = \/... | |
 | William Findlay Shunk - 1880 - 362 pàgines
...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, by using simple... | |
 | George Albert Wentworth - 1881 - 400 pàgines
...logarithm of m. Then m = a 1 , and TTI* = (a z )p = a***. .'. log mf = px, IV. 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 x be the logarithm of in. Then m = a x , and m* - . («*/ = of 319. An exponential equation,... | |
 | George Albert Wentworth - 1881 - 406 pàgines
...be the logarithm of m. Then m = a", and mf = (a*)r = of. .'. log mf =px, IV. 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 x be the logarithm of m. Then m = a x , and m r = (a x ) = a r . lj « 319. An exponential... | |
 | Edwin Pliny Seaver, George Augustus Walton - 1882 - 322 pàgines
...root, }/N=b«, •whence it appears (Art. 384) that - is the logarithm of i/N. 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) \o%(NN'N" . . .)... | |
 | Edwin Pliny Seaver, George Augustus Walton - 1882 - 308 pàgines
...root, %N= 6", whence it appears (Art. 384) that - is the logarithm of ^N. 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) logC^JV' N" . .... | |
 | Simon Newcomb - 1882 - 302 pàgines
...»th power, 10"" = p n . Whence nh — logjo", or n log/; = lojp n . THEOREM X. TJie 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 n . Hence log s —... | |
 | George Albert Wentworth, Thomas Hill - 1882 - 376 pàgines
...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 = Jx 0.3010 = 0.0753. log .002* = J... | |
 | George Albert Wentworth, Thomas Hill - 1882 - 376 pàgines
...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. Thua, log 2* = J of log 2 = Jx 0.3010 = 0.0753. log .002* = J... | |
 | George Albert Wentworth - 1883 - 536 pàgines
...the logarithm of m. Then m = a', and m" =• (a']r = a"*. .'. log TO* = px, IV. 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 x bo the logarithm of m. Then m = OP, and m — (off = of. 319, An exponential equation, that... | |
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the logarithm of the m th root of a number is equal to the logarithm of the number divided by the index of the root LOGARITHMS. 
