 | 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 - 674 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... | |
 | John Charles Stone, James Franklin Millis - Algebra - 1905 - 776 pages
...Then np = (a* )" = <#*». Hence, \oganp = px= p lognw. (F) T/ie logarithm of a root of a number equals the logarithm of the number, divided by the index of the root; that is, r — log,,n To prove this, let ax—n. is Then i/n=yax—ar. r — X lug.« 1 , Hence, log,,in=-... | |
 | Webster Wells - Algebra - 1906 - 484 pages
...af* = mr; whence, ]og„mp=px=p logem. 424. In any system, the logarithm of any root of a number in equal to the logarithm of the number divided by the index of the root. ii For, log. \/т = loge(m--) = -logam (§ 423). 425. Examples. 1. Given log 2 = .3010 ; find log 2*.... | |
 | Arthur Schultze - Algebra - 1906 - 584 pages
...log n*= /?log я. Eg log 2U = 10 log 2; log J = log 2-3 = -Slog 2 ; 9. The logarithm of a root of a number is equal to the logarithm of the number divided by the index. p-1 P Eg log ^7 = t log 7. Ex. 1. Given log 2 = .30103, and log 3 = .47712, find log 288. log 288 =... | |
 | Webster Wells - Algebra - 1906 - 550 pages
...powei, apx = mp; whence, loga m? =px =p loga m. 424. In any system, the logarithm of any root of a number is equal to the logarithm of the number divided by the index oj the root. For, logaVm = log.(m'-) = };log0m (§ 423). 425. Examples. 1. Given log 2 = .3010 ; find... | |
 | George Albert Wentworth - Algebra - 1906 - 440 pages
...cologarithm N = log N = log 1 - log N = 0 - log N = -logN = (10 -log N)- 10. Hence, the cologarithm of a given number is equal to the logarithm of the number with the minus sign prefixed, and the negative sign affects the entire logarithm. 463. To avoid a negative... | |
 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...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. . 6. The preceding principles enable us to abridge labor in arithmetical calculations, by using simple... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...pth power, ap*—иlp. whence, Iog„mp=px=j9logam. 90. In any system, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. — - 1 For, log„Vm = lo&,(m;)=~ logam(§ 89). 91. Examples. 1. Given log 2 = .3010 ; find log 2Í... | |
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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. 
