 | Simon Newcomb - Algebra - 1882 - 302 pages
...Raising both sides to the иth power, 10"* = p". Whence nh — log jo", or n log p = logy. THEOREM X. The 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". Hence log s = logp"... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...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. RULE. Add... | |
 | Simon Newcomb - Logarithms - 1882 - 204 pages
...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. KULE. Add... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 376 pages
...3" = 11 X log 3 = 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 2J = | of log 2 = } X 0.3010 = 0.0753. log .002* = J... | |
 | George Albert Wentworth - 1883 - 536 pages
...be the logarithm of m. Then т = а*, and mr = (a*yr = af. .-. log mP = px, IV. The logarithm of the root of a number is equal to the logarithm of the number divided by thе index of the root. For, let x be the logarithm of m. Then m = of, and m = (aff = cff. 319. An... | |
 | Stephen Roper - Mechanical engineering - 1884 - 740 pages
...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... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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 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... | |
 | Edward Brooks - Algebra - 1888 - 344 pages
...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 *_!**;... | |
 | Edward Albert Bowser - Algebra - 1888 - 868 pages
...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 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
...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 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,... | |
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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. 
