 | Joe Garner Estill - 1896 - 168 pàgines
...equal to the logarithm of the number multiplied by the exponent of the power. IV. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. 3. The only kind of logarithms with which we have to do here are those in which the assumed number,... | |
 | James William Nicholson - 1898 - 204 pàgines
...the power. For, Art. 2, (/)', a* = l0"'. ... (Art. 1), logai=pa', or by (A), log a" =px loga. 5. lV. The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root. For, Art. 2, • V(f), .Vä = l 0"r . r - a' .•. (Art. 1), logVä = — > or by (A), log л/а =... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - 1899 - 506 pàgines
...numerator is 1, this principle may be conveniently stated thus : The logarithm of a root of a number is the logarithm of the number divided by the index of the root. ,ir For, logi (m') = llog m = Ч Ч Eg, If Iog7 2401 = 4, what is Iog7 V2401 ? We have Iog7 V2401 =... | |
 | Elmer Adelbert Lyman, Edwin Charles Goddard - 1899 - 188 pàgines
...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 if ax = n and av = m, then nxm = ax+v, .•. logwm = x + y = logn + logm; and n .t. m = ax~v, .'.log—... | |
 | Webster Wells - 1906 - 484 pàgines
...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*.... | |
 | Webster Wells - 1908 - 456 pàgines
...the assumed equation to the pth power, ap*—иlp. whence, Iog„mp=px=j9logam. 90. In any system, the logarithm of any root of a number is equal to...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... | |
 | William Findlay Shunk - 1908 - 386 pàgines
...power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to...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... | |
 | Frederick Howland Somerville - 1908 - 428 pàgines
...logmf=px. 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, log... | |
 | William James Milne - 1908 - 476 pàgines
...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,... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1908 - 520 pàgines
...logarithm of the dividend minus the logarithm of the divisor. (b) The logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log 2 = loga — log b and log л/о = D П EXERCISES By means of logarithms approximate the... | |
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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. 
