 | 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... | |
 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...But, from (1), x = log m, , (Art. 438) Hence, log m" = pQog "0 • 456. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let 10« = m. (1) Raising both members to the power indicated by -, x 1 9 10« = m«. •1 Whence,... | |
 | William James Milne - Algebra - 1908 - 476 pages
...logarithms are simply exponents, it follows that : 587. PRINCIPLE. — The logarithm of a root ofanumber is equal to the logarithm, of the number divided by the index of the required root; that is, To any base, log -л/ni =Ж^. и For, let log,, in = x and let n be any number,... | |
 | John Charles Stone - Business mathematics - 1908 - 266 pages
...nf = (a°)r = a?'. Hence, log a nf = px = p logo n. IV. The logarithm of a root of a number equals the logarithm of the number, divided by the index of the root. For let a I =?i. r,- ,v—• Then, v n=ya'=a r . EXAMPLE 1. Iogio30=logio2x3x5=log 1 o2+logio34-logi... | |
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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. 
