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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 - 1890 - 339 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

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

William Findlay Shunk - 1880 - 318 páginas
...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...
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