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 Βιβλία Βιβλία 41 - 50 από 99 για The logarithm of any power of a number is equal to the logarithm of the number multiplied....
The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
A Theoretical and Practical Arithmetic: In which the Principles of that ... - Σελίδα 233
των Bézout - 1825 - 236 σελίδες
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An Elementary Algebra

Daniel Barnard Hagar - 1873 - 263 σελίδες
...equation a" = n, member by member, we have in which x— y is the logarithm of the quotient — . 5. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, raising both members of the equation ax =...

Elements of Algebra

...if»>m, loga is negative, ie the logarithm of a number less than unity is negative. 160. — PROP. The logarithm of any power of a number is equal to the logarithm of the number, multiplied by the index of the power. For if x = log . га, я = о*, . • . nm = a1"*...

Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - 1864 - 490 σελίδες
...12.234 : 87.5 X 3.7547 : : 56.5 : r, to find z. Ans. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of thc power. Let (1) b* =n; then, by def., log n =z. (1)'=(2)...

Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1874 - 455 σελίδες
...to the power denoted by p, we have, 10'' = mr ; whence, by the definition, xp = log mr (8.) That is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both...

The Complete Algebra: Designed for Use in Schools, Academies, and Colleges

Joseph Ficklin - 1874 - 418 σελίδες
...subtracting the logarithm of the divisor from that of the dividend. Dividing m = a* by n = 0", 562. The logarithm of any power of a number is equal to the product of the exponent of the power and the logarithm of the number. Kaising both members of the equation...

Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - 1875 - 184 σελίδες
...12.234 : 87.5 X 3.7547 : : 56.5 : x, to find x. Ans. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Let (1) bz =и; then, by def., log n =x. (1)*=(2)...

New University Algebra

Horatio Nelson Robinson - 1875 - 412 σελίδες
...= log. w. 771 By division, — = a" ; n therefore, log. I — ) = x — z = log. 7W — log. n. 5. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, let m=cf; then z = log. m. By involution,...

Manual of Algebra

William Guy Peck - 1875 - 331 σελίδες
...have, aP* = mp; whence, by definition, px — Log mp; . . . . (7) hence, the following principle: 3°. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. If we extract any root of both members of (3),...

Elementary Arithmetic: With Brief Notices of Its History, Τόμοι 1-12

Robert Potts - 1876
...«logc" by def. Then raising each to the »ih power. a• = a-dogi«. .•. loga{«•} = n loga«. Or, the logarithm of any power of a number, is equal to the product of the logarithm of the number and the index of the power. 5. PEOP. To find the logarithm of...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1876 - 170 σελίδες
...member by member, we have .М_а^_ . N — a« Therefore, log f-^Л =x — y= log M — log Ж 11. The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take...