...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....

...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....

...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...

...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...

...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...

...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...

...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...

...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, -...

...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),...

...and 2, as docs the logarithm of 74. 5. The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. The logarithm...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...