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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 73
by Nathan Scholfield - 1845
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...have mr = an; therefore, log. (mr) = rx = r log. m. 6. — The logarithm of any root of a number ù equal to the logarithm of the number divided by the index of the root. For, let то = a1 ; then x = log. от. • By evolution we have \Ara = <f ', x log. m therefore,...
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Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 288 pages
...a"» = <* УBut, ^ = log tj/"y7and x = log y. Hence «lo That is, the logarithm of the m"1 root of a number is equal to the logarithm of the number divided by the index of the root. LOQABITHlfS. 5 and then finding in the tables the number whoso logarithm is equal to the sum or difference,...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...have, 10"- = JM* Hence, log M n = mn, or, = log M X n. PRIN. 7. — The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. For, since 10" = M, if we take the nth root of both members, we have, Hence, log .\/~M= — , or, log...
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Elements of Surveying and Leveling; with Descriptions of the Instruments ...

Charles Davies - 1871 - 458 pages
...1CT = ym; whence, by the definition, I = log j/^. ...... (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 ns to abbreviate the operations of multiplication and division of numbers,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1871 - 492 pages
...have, 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 at1ons of multiplication and division, by...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...have, • «d' = \/m ; whence, by the definition, ~ .... (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. TABLE OB LOGARITHMS. 9. A TABLE OF LOGARITHMS, is a table containing a set of numbers and their logarithms,...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 506 pages
...power of .9. Ans. .59047. 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. lX(l) = (2) b'r —1/n; then, by def., log 1</~^, = — ....
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Elements of Algebra

Charles Elsee - 1873
...above proof be considered fractional ( = - J, we have also ^ = 7 1ов.». ic the logarithm of a root is equal to the logarithm of the number, divided by the index of the root. 161.— PROP. Logawi = Log,,™ x Logai. For let logb m = y, and log„ Ь = z, then m = Ъ", Ь =...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...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 and division, by...
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Appleton's Dictionary of Machines, Mechanics, Engine-work, and ..., Volume 2

Mechanical engineering - 1874
...have log. y* (or log. */ y) = — log. y ; that is to say, the logarithm of any root of a number ia equal to the logarithm of the number divided by the index of the root. From these two last results it is obvious that by means of a table of logarithms numbers may be raised...
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