 | Aaron Schuyler - Navigation - 1873 - 536 pages
...Ans. 525.55. 5. Find the fifth power of .9. .Ans. .59049. EVOLUTION BY LOGARITHMS. 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. = (2) b'r —\/n; then, by def., log... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...members of (4), we have, 10r = whence, by the definition, * = log 'Jm. ' • • • ( 9.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. The preceding principles enable us to abbreviate the oper ations of multiplication... | |
 | Charles Davies - 1874 - 464 pages
...of both members of ( 4 ), we have, whence, by the definition, " = log^ . • • • (9.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by t/1e index of tie root. TABLE OF LOGARITHMS. 9. A TABLE OF LOGARITHMS, is a table containing a set... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...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 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... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...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 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.... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...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... | |
 | Benjamin Peirce - 1875 - 306 pages
...becomes • log. p = n log. v/ p, log. ^ p = fc**; n that is, the logarithm of any roof, of a number 's equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. The equation log. m m' = log. m + log. m' t gives log. m' = log. m m' — log. m; that... | |
 | Robert Potts - Arithmetic - 1876 - 392 pages
...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... | |
 | Robert Potts - Arithmetic - 1876 - 389 pages
...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... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 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... | |
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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. 
