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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. "
Encyclopaedia Perthensis; Or Universal Dictionary of the Arts, Sciences ... - Página 323
1816
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Surveying and Navigation: With a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1873 - 482 páginas
...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...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 455 páginas
...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...
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Elements Of Geometry And Trigonometry

Charles Davies - 1874
...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...
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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 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...
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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 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....
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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...
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Elementary Treatise on Algebra

Benjamin Peirce - 1875
...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...
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Elementary Arithmetic: With Brief Notices of Its History, Volumes 1-12

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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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...
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