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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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The London encyclopaedia, or, Universal dictionary of ..., Volume 13,Parte 1

Thomas Curtis (of Grove house sch, Islington)
...a number is equal to the logarithm of that number, multiplied by the exponent of the power ; also, that the logarithm of any root of a number is equal...the exponent of the root. 42. There may be various systems of logarithms, according to the different values which may be given to the number r, which...
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A system of popular trigonometry

George Darley - 1835
...logarithm of the number multiplied by the index of the power, 8. AHT. 6. The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root, 9. . THE APPLICATION OF ALGEBRA TO GEOMETRY. DEF. The area of a figure is the .portion...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1837 - 288 páginas
...substitute m = Vp, in the above equation, it becomes log. p = n log. or , " log. n log. V>= -~n that is, the logarithm of any root of a number is equal to...of the number divided by the exponent of the root. 11. Corollary. The equation log. m m' = log. m -f log. m', gives log. m' = log. mm' — log. m ; that...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1837 - 276 páginas
...= */p, in the above equation, it becomes n log. p = » log. V>, or * log! p log- Vp = *&* that is, the logarithm of any root of a number is equal to...of the number divided by the exponent of the root. 11. Corollary. The equation log. m m' = log. m + log. m', gives log. m' = log. mm' — log. m ; that...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1837 - 288 páginas
...*»", • m = in the above equation, it becomes log. p = n log. or " log. p log. VP = =3* that is, </ie logarithm of any root of a number is equal to the logarithm of the number divided by the expon ent of the root. 11. Corollary. The equation log. mm' = log. m -f log. m,, gives log. m, = log....
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A Treatise on Trigonometry, and on Trigonometrical Tables and Logarithms ...

John Hymers - 1841 - 151 páginas
...where r is any number whole or fractional, positive or negative. 10. The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. Since т ч cf, .: <t/m •» v/0* = ar, _ л i * * De V " / — V Oft r* TT 11....
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1843 - 284 páginas
...substitute m — -/p, in the above equation, it becomes log. p — n log. log. S p = ISLJL; n that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the ezponent of the root. 13. Corollary. The equation log. m mf = log. m 4- log. m', gives log. m' = log....
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Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ...

William Chauvenet - 1843 - 92 páginas
...of the number by the exponent of the power; the product is the logarithm of the required power. 63. The logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. For to extract the nth root of the equation a1-**—...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845
...JL .: by def. (2), — is the logarithm of N » that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the two last cases, we shall find, whence, — is the logarithm of N "•"....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 232 páginas
....: by def. (2), — is the logarithm of N •> that is to say, The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the two last cases, we shall find, m in v N~r = a~ whence, — is the...
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