 | George Washington Hull - 1895 - 358 páginas
...logf 10. log'-0/. 15. loglTV. 20. log 17/s. 6. log A11. log--°Ty-. 16. logSf. 21. k>g23t)i§. 277. The logarithm of any root of a number is equal to the logarithm of the quantity divided by the index of the root. Let m be any number, and x its logarithm. Then, by definition,... | |
 | Joe Garner Estill - 1896 - 168 páginas
...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,... | |
 | Joe Garner Estill - 1896 - 186 páginas
...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 páginas
...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 =... | |
 | Webster Wells - 1906 - 484 páginas
...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*.... | |
 | William Findlay Shunk - 1908 - 386 páginas
...the mixed number 74.103 lies between 10 and 100; hence its logarithm lies between 1 and 2, as does the logarithm of 74. 5. The logarithm of the product...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 - 1908 - 456 páginas
...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... | |
 | Frederick Howland Somerville - 1908 - 428 páginas
...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,... | |
 | William James Milne - 1908 - 476 páginas
...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 - 1908 - 266 páginas
...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. 
