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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. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 75
by Nathan Scholfield - 1845
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Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

John Charles Stone, James Franklin Millis - Algebra - 1905 - 792 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=-...
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Algebra for Secondary Schools

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*....
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Advanced Algebra

Arthur Schultze - Algebra - 1906 - 562 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 =...
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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 570 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...
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Elementary Algebra

George Albert Wentworth - Algebra - 1906 - 421 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...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1908 - 345 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...
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A First Course in Algebra ; A Second Course in Algebra

Webster Wells - Algebra - 1908 - 470 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 2...
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Elementary Algebra

Frederick Howland Somerville - Algebra - 1908 - 407 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,...
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Standard Algebra

William James Milne - Algebra - 1908 - 464 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,...
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A Secondary Arithmetic

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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