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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. "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 81
by Nathan Scholfield - 1845 - 232 pages
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New University Algebra

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 - 284 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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Elements of Plane and Spherical Trigonometry: With Practical Applications

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 the nth root of both...
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New Elementary Algebra

Benjamin Greenleaf - 1879 - 346 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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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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The Field Engineer: A Handy Book of Practice in the Survey, Location, and ...

William Findlay Shunk - Railroad engineering - 1880 - 362 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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Elements of Plane and Spherical Trigonometry with Logarithmic and Other ...

Simon Newcomb - Trigonometry - 1882 - 372 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. RULE. Add...
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The Franklin Elementary Algebra

Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...b", whence it appears (Art. 384) that is the logarithm of y/jV. Hence The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. 395. Briefly expressed in formulas the propositions just proved are as follows: (1) }og(NN'N" . . .)...
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Logarithmic and Other Mathematical Tables: With Examples of Their Use and ...

Simon Newcomb - Logarithms - 1882 - 204 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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