| Horatio Nelson Robinson - 1875 - 430 páginas
...power. For, let m=cf; then z = log. m. By involution, m' = a" ; therefore, log. (mr) =rx = r log. m. 6. The logarithm of any root of a number is equal to...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 - 1875 - 284 páginas
...Ans. 525.55. 5. Find the fifth power of .9. Am. .59047. I EVOLUTION BY LOGARITHMS. f 25. Proposition. The logarithm of any root of a number is equal to...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 - 1875 - 348 páginas
...we have, ar = whence, by 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 - 1876 - 204 páginas
...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... | |
| Robert Potts - 1876 - 389 páginas
...the logarithm of any root of a numi er. Here u = d°s* u by def. Andlog a {V 7l } = »jloga«. Or, the logarithm of any root of a number, is equal to the quotient arising from dividing the logarithm of the number by the index of the root. Hence it appears... | |
| Robert Potts - 1876 - 392 páginas
...the logarithm of any root of a number. Here M = я1c8«« by def. And log. {и*} = ,flog„«. Or, the logarithm of any root of a number, is equal to the quotient arising from dividing the logarithm of the number by the index of the root. Hence it appears... | |
| Benjamin Greenleaf - 1879 - 346 páginas
...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, -... | |
| Benjamin Greenleaf - 1879 - 322 páginas
...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... | |
| Elias Loomis - 1879 - 398 páginas
...the exponent "of the power ; the product is the logarithm of the required power. 399. The loganlhm of any root of a number is equal to the logarithm of that number divided by the index of the root. If we extract the rth root of both members of Eq. (1),... | |
| William Findlay Shunk - 1880 - 362 páginas
...the mixed number 74.103 lies between 10 and 100; hence its logarithm lies between 1 and 2, as docs the logarithm of 74. 5. The logarithm of the product...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... | |
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