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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. "
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 4
por William Findlay Shunk - 1880 - 318 páginas
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 184 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....
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - 1875 - 412 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....
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Manual of Algebra

William Guy Peck - 1875 - 331 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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1876 - 170 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...
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Elementary Arithmetic: With Brief Notices of Its History, Volúmenes1-12

Robert Potts - 1876
...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...
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ELEMENTARY ARITHMETIC, WITH BRIEF NOTICES OF ITS HISTORY

ROBERT POTTS - 1876
...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...
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New Elementary Algebra: Designed for the Use of High Schools and Academies

Benjamin Greenleaf - 1879 - 309 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...
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New Elementary Algebra

Benjamin Greenleaf - 1879
...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, -...
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A Treatise on Algebra

Elias Loomis - 1879 - 384 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),...
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Roper's Questions and Answers for Engineers

Stephen Roper - 1880 - 63 páginas
...Any root of any number may be found by logarithms as follows : The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. Hyperbolic logarithms is a system of logarithms, so called, because the numbers express the areas between...
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