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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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 páginas
...have Mm = (a*)"1 = a™ . Therefore, log (Mm) = xm = (log M) X m. 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) Therefore, log 13. Hence,...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1864 - 284 páginas
...we substitute in the above equation, it becomes log. p = n log. or log. ^/ p = — -I n that is, /Ac logarithm of any root of a number is equal to the...of the number divided by the exponent of the root. 13. Corollary. The equation log. TO TO' = log. TO + log- *»', gives log. TO' = log. mm! — log. TO...
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A Treatise on Algebra

Elias Loomis - 1864 - 359 páginas
...obtain I Nm=am ; therefore, according to the definition, — is the logarithm of Nm; hence PROPERTY IV. The logarithm of any root of a number is equal to the logorithm of that number divided by the index of the root. EXAMPLES. Ex. 1. Find the square root of...
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Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 páginas
...shall have 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...
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A Treatise on Elementary Algebra

James Hamblin Smith - 1869
...logarithm of the number and the index denoting the power. Let m = a*. Then mr = a" = r . log m. 374. The logarithm of any root of a number is equal to the quotient arising from the division of the logarithm of the number by the number denoting the root....
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Elementary Trigonometry

James Hamblin Smith - 1870 - 224 páginas
...proceed thus log 13 = 1-1139434 4 4-4557736 which is the logarithm of 28561, the number required. 147. The logarithm of any root of a number is equal to the quotient arising from the division of the logarithm of the number by the number denoting the root....
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Elementary Algebra

James Hamblin Smith - 1870
...proceed thus, log 13= 1-1139434 4 4-4557736 which is the logarithm of 28561, the number required. 458. The logarithm of any root of a number is equal to the quotient arising from the division of the logarithm of the number by the number denoting the root....
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Elements of Surveying and Levelling: With Descriptions of the Instruments ...

Charles Davies - 1871 - 431 páginas
...both members of (4), we have, 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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 58 páginas
...Required the seventh power of 0.8952. EVOLUTION BY LOGARITHMS. (15.) It is proved in Algebra, Art. 341, that the logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. Hence, to extract tfot -cot of a number by logarithms,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1872 - 455 páginas
...of both members of ( 4 ), we 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...
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