 | Aaron Schuyler - Navigation - 1873 - 536 pages
...2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is egual to the logarithm of the number multiplied by the exponent of the power. Let (1) b• =n; then, by def., log n =x. (1y=(2) b"=n'; then, by def., log n'=p . • . log n' = p... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...of (4) 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...the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of (4), we have, 10r = whence, by the definition,... | |
 | Joseph Ficklin - Algebra - 1874 - 446 pages
...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... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...= 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 number multiplied by the exponent of the power. For, let m=cf; then z = log. m. By involution, m' = a" ; therefore, log. (mr) =rx = r log. m. 6. The... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...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 number multiplied by the exponent of the power. If we extract any root of both members of (3), denoted by r, we have, ar = whence, by definition, ^... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...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 number multiplied by the exponent of the power. Let (1) bz =и; then, by def., log n =x. (1)*=(2) 6"x=n!'; then, by def., log n'—px. . • . log... | |
 | Benjamin Peirce - 1875 - 306 pages
...Logarithm of Root, Quotient, and Rec'procal. that is, the logarithm of any power of a number is < >/>i<> / to the logarithm of the number multiplied by the exponent of the power. 12. Corollary. If we substitute p = m", or m— v//;, in the above equation, it becomes • log. p = n log. v/ p, log. ^ p = fc**; n... | |
 | Robert Potts - Arithmetic - 1876 - 418 pages
...«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... | |
 | Robert Potts - Arithmetic - 1876 - 392 pages
...eloe«« by def. Then raising each to the wlh power. a' = «"log««. .-. log„{«"} = » log.«. 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. PB.OP. To find the logarithm... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...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... | |
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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. 
