 | Isaac Todhunter - Plane trigonometry - 1875 - 250 pages
...therefore log«- - = x — y = log„m — log.n. 55. The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number and the index of the power,For let m = a"; therefore m- = (a")' = a", therefore log„(mf)=rx=r iog.m.... | |
 | 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 logarithm of the number multiplied by the exponent of the power. If we extract any root of both members... | |
 | 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 logarithm of the number multiplied by the exponent of the power. Let (1) bz =и; then, by def., log... | |
 | 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 logarithm of the number multiplied by the exponent of the power. For, let m=cf; then z = log. m. By... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...second, 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...let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) =... | |
 | 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 any root of a numbcr. Here u = alosc«... | |
 | 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 of any root of a number. Here M = я1c8««... | |
 | James Hamblin Smith - Trigonometry - 1877 - 244 pages
...17191323 their difference = -8508148 which is the logarithm of 7'092752, the quotient required. 149. Tfie logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power, Let m = a*. Then mr=a,n; .:logamr=rx =r.log0«i. Thus the operation... | |
 | Edward Brooks - Arithmetic - 1877 - 564 pages
...by the second, we have, »•— f Hence, log ( — J = m — n, or, = log M — log N. PRIN. 6. — The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, since if we raise both members... | |
 | Benjamin Greenleaf - Algebra - 1879 - 376 pages
...equations, ax = m, a" = n, and dividing, member by member, we have , „ in ax~>> — — n (V »/' 3fiO. The logarithm of any power of a number is equal to the logarithm of the number, multiplied by the exponent of the power. For, assume the equation, a* = m,... | |
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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 the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a""... 
