 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 520 pages
...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... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 216 pages
...logarithm of the dividend minня the logarithm of the divisor. (b) Tlie logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log Y = log a — log b and log л/о = Y D n EXERCISES By means of logarithms approximate... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 272 pages
...(a1)»1 = apx or, loga (n?) =px = p log« n. * (3) IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, if x = loga и, then n = a". Extracting the qth root of both members, we get = a«, whence, log« A/M.... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...(a1)" = ap* or, log« (n'») = px = p loga n. (3) IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, if x = loga n, then n = ax. Extracting the <?th root of both members, we get V71 = яi, whence, logaí/ñ... | |
 | Charles E. Larard, Henry A. Golding - Engineering - 1909 - 508 pages
...multiplied by the index of the power, and also that the logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. This is the mathematical principle underlying the determination of powers and roots by means of the... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...= (10*)" = 10*». .'. log m v = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. i -?/— —® — log m yy ' X 6. The logarithm of any integral power or root of 10 is an integral... | |
 | Levi Leonard Conant - Plane trigonometry - 1909 - 290 pages
...mv = (10*)" = 10*y. .'. log mv = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. x PROOF. VTO = Vl& = 10". , y, — X log m .'. logvm = - = — — . yy 6. The logarithm of any integral... | |
 | William Charles Brenke - Algebra - 1910 - 374 pages
...exponent of the power times the. logarithm of the number.. IV. The logarithm of any root of à number equals the logarithm of the number divided by the index of the root. (Rule III contains rule IV, since the power in question may be fractional.) 40. The following facts... | |
| |
The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
