 | William James Milne - Algebra - 1902 - 620 pages
...logarithms are simply exponents, it follows that : 482. PRINCIPLE. — The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the required root; that is, To any base, log -v/m = ^^n The above principle may be established as follows:... | |
 | Thomas Ulvan Taylor, Charles Puryear - Trigonometry - 1902 - 248 pages
...Therefore, log a w p =^a:, or, substituting for x its value, (d) The logarithm of a root of a number equals the logarithm of the number divided by the index of the root. Thus, Prcof. Let n be the number and r the index of the root. Then, log a Vw = log a n~ r = - log a... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 392 pages
...l°ga (™p) = px Substituting for x its value, loga (»i?) = p loga m 64. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. By algebra, Therefore, by Art. 63, 65. A few examples will illustrate these principles. Given that... | |
 | John Marvin Colaw - Algebra - 1903 - 444 pages
...7. 1.073. 10. .3213. 13. .03928. 5. 782. 8. .0282. 11. 5745. 14. 482. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. Thus, VI00OO = Vl04 = 10^. .-. log VlO0O0 = 4 -=- 2 = 2. In general, if log m = x and a = any root... | |
 | James Morford Taylor - Plane trigonometry - 1904 - 192 pages
...px=p logalf. (1) If p = 1/r, from (1) it follows that (iv) The logarithm of any root of an arithmetic number is equal to the logarithm of the number divided by the index of the root. An expression is said to be adapted to logarithmic computation when it involves only products, quotients,... | |
 | Henry Burchard Fine - Algebra - 1904 - 616 pages
...(aT-)r = a*r, that is, logamr = r/j. = r Iog0m. 739 Theorem 4. The logarithm of any root of a number is the logarithm of the number divided by the index of the root. For if m = a1*, ,_ . — Ü we have vm = Va** = о* , that is, log« V»t = p/ s = (log„m)/s. 740... | |
 | Henry Burchard Fine - Algebra - 1904 - 612 pages
...(aT)' = a*', that is, logamr = rц = r loga»i. 739 Theorem 4. The logarithm of any root of a number is the logarithm of the number divided by the index of the root. For if m = <Р, •г- Ч— we have vm = vaм = a', that is, loga^m = ц /s = (logam)/s. 740 The practical... | |
 | James Morford Taylor - Trigonometry - 1905 - 256 pages
...p loga M. (1) If p = l/r, from (1) it follows that (iv) The logarithm of any root of an arithmetic number is equal to the logarithm of the number divided by the index of the root. An expression is said to be adapted to logarithmic computation when it involves only products, quotients,... | |
 | Arthur Schultze - Algebra - 1905 - 694 pages
...= log 2-8 = - 3 log 2 ; log ?-X-?Í = log 2 + 3 log 7 - 5 log 2 ; 9. TJie logarithm of a root of a number is equal to the logarithm of the number divided by the index. log л/л = log я* = - log a. (§ 8) P Eg log </l = I log 7. Ex. l. Given log 2 = .30103, and log... | |
 | Elmer Adelbert Lyman - Arithmetic - 1905 - 270 pages
...equals the index of the , power times the logarithm of the number. IV. The logarithm of a root equals the logarithm of the number divided by the index of the root. For let 10* = n and 10» = m, then log n = x and log m = y. Therefore, since mn = lO'+o, log mn = x... | |
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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. 
