 | 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... | |
 | 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... | |
 | Charles E. Larard, Henry A. Golding - Engineering - 1909 - 508 pages
...the number itself 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... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 272 pages
...ax. Hence, np = (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«... | |
 | Levi Leonard Conant - Plane trigonometry - 1909 - 290 pages
...the power. PROOF. 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... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...a*. Hence, np = (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,... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...the power. PROOF. m? = (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... | |
 | Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 212 pages
...(6•)» = J~, or logs (mn) =nx. But , x = logs m; logs m n = n- log s m. VI. T^e logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let m=b x , or logsm=a;; then or n * VII. The logarithm of a proper fraction is always a negative number,... | |
 | William Charles Brenke - Algebra - 1910 - 376 pages
...of the power times the. logarithm of the number.. IV. The logarithm of any root of ŕ 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... | |
 | Herbert E. Cobb - Mathematics - 1911 - 298 pages
...log V3 = log 3* = J log 3. V3 = 3* = (10°-4771)* = 10°-2886 = 1.732. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. PROBLEMS 1. Multiply 28.34 by 3.376. log 28.34 = 1. log 3.376 = 0. Before finding the mantissas from... | |
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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. 
