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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.
Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ... - Pągina 22
per Aaron Schuyler - 1864 - 490 pągines
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volum 13

1816
...number is equal to the logarithm of that number, multiplied by the exponent of the power ; alfo, that the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. (42.) There may- be various fyftems of logarithms, according to the different...
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The London encyclopaedia, or, Universal dictionary of science, art ...

Thomas Curtis (of Grove house sch, Islington)
...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 to the logarithm of the number divided by the exponent of the root. 42. There may be various systems of logarithms, according to the different values...
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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 of space contained...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1837 - 276 pągines
...= */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 the logarithm 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....
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - 1837 - 288 pągines
...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 the logarithm 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....
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An elementary treatise on algebra: to which are added exponential equations ...

Benjamin Peirce - 1837 - 288 pągines
...*»", • 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 pągines
...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. Hence, if we have...
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Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ...

William Chauvenet - 1843 - 92 pągines
...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 "•". n It is of the...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

1845
....•. 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, •fjj T~ nk whence, — is the logarithm of N "»". 4...
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