| 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 - 374 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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