| Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...m. By involution, m' = a" ; therefore, log. (mr) =rx = r log. m. 6. The logarithm of any root of a **number is equal to the logarithm of the number divided by the index of the root.** For, let m = a' ; then x — log. m. • By evolution, A/m = a' ; ,, , r,— x log. m therefore, log.... | |
| Aaron Schuyler - Measurement - 1875 - 276 pages
...power of .9. Am. .59047. I EVOLUTION BY LOGARITHMS. f 25. Proposition. The logarithm of any root of a **number is equal to the logarithm of the number divided by the index of the root.** Let (1) b' = n; then, by def., log n = x. V(l) = (2) br =\/n; then, by def., log Vх n = — • r.... | |
| William Guy Peck - Algebra - 1875 - 348 pages
...definition, ^ = Log tfm .... (8) hence, the following principle: 4°. Tlie logarithm of any root of a **number is equal to the logarithm of the number divided by the index of the root.** The applications of the above principles require a table of logarithms. A table of logarithms, is a... | |
| Benjamin Greenleaf - Trigonometry - 1876 - 208 pages
...have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12. The logarithm of the ROOT of any **number is equal to the logarithm of the number divided by the index of the root.** For, let n be any number, and take the equation (Art. 9) M=a*, then, extracting the nth root of both... | |
| Benjamin Greenleaf - Algebra - 1879 - 322 pages
...members to the power p, we have ax" = mP, in which xp = logn m p. 361. The logarithm of the root of any **number is equal to the logarithm of the number, divided by the index of the root.** For, assume the equation, ax = m, and extracting the rth root of both members, we have, a'= $ m, in... | |
| Benjamin Greenleaf - 1879 - 348 pages
...to the power p, we have <ff = mp, in which xp = loga m f. 361 • The logarithm of the root of any **number is equal to the logarithm of the number, divided by the index of the root.** For, assume the equation, c?= m, and extracting the rth root of both members, we have, in which, -... | |
| William Findlay Shunk - Railroad engineering - 1880 - 318 pages
...the logarithm of 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.** 0. The preceding principles enable us to abridge labor in arithmetical calculations, by using simple... | |
| Stephen Roper - Steam engineering - 1880 - 84 pages
...use. Any power of a given number may be found by logarithms as follows : The logarithm of any power **of a given number is equal to the logarithm of the number** multiplied by the exponent of the power. EXAMPLE.— To find the fifth power of 9, logarithm 9 = 0-954243X5... | |
| Simon Newcomb - Algebra - 1882 - 304 pages
...power, 10"* = p". Whence nh — log jo", or n log p = logy. THEOREM X. The logarithm of a root of a **number is equal to the logarithm of the number divided by the index of the root.** Proof. Let s be the number, and let p be its nth root, so that p = VU and s = p". Hence log s = logp"... | |
| Simon Newcomb - Logarithms - 1882 - 208 pages
...logarithm of the number multiplied by the exponent of the power. IV. The logarithm of the root of a **number is equal to the logarithm of the number divided by the index of the root.** We thus derive the following rules: To find the product of several factors by logarithms. KULE. Add... | |
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