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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 Geometry: With Practical Applications to Mensuration - Page 2
by Benjamin Greenleaf - 1863 - 320 pages
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Advanced Arithmetic

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 + y = log...
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Advanced Algebra

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...
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Essentials of Algebra: Complete Course (an Adequate Preparation for the ...

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=-...
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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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Algebra for Secondary Schools

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...
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Advanced Algebra

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 =...
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A First Course in Algebra ; A Second Course in Algebra

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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Elementary Algebra

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,...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1908 - 388 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 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 0 6....
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