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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. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 75
by Nathan Scholfield - 1845
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

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....
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Plane and Spherical Trigonometry and Mensuration

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....
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Manual of Algebra

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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New Elementary Algebra: Designed for the Use of High Schools and Academies

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...
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New Elementary Algebra

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, -...
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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

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...
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Roper's Questions and Answers for Engineers

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...
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A School Algebra

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"...
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Logarithmic and Other Mathematical Tables: With Examples of Their Use and ...

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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