| Benedict Sestini - Algebra - 1857 - 258 pages
...xc ; but from a"= z, we have x = lz ; hence, l.<f= cl.z; that is, The logarithm of the power of any **number is equal to the logarithm of the number multiplied by the exponent.** But if we take the root of the degree c of both members and consequently, lz' = - = -x; - x 1 cc now... | |
| Benjamin Peirce - Algebra - 1858 - 296 pages
...if they are all equal to each other, we have log. mmm &-c. = log. m -j- log. m -f- log. m -j- &c. or **Logarithm of Root, Quotient, and Reciprocal. that...the number multiplied by the exponent of the power.** 12. Corollary, If we substitute p = mn, or m = \/P, in the above equation, it becomes n log. p = n... | |
| William Smyth - Algebra - 1858 - 344 pages
...raismg both members to the with power, we have a~ = 1r; whence the logarithm of y m = mx = m log y. **That is, the logarithm of any power of a number is equal to the** product of the logarithm of this number by the exponent of the power. To form any power whatever of... | |
| Elias Loomis - Algebra - 1858 - 392 pages
...Nm, since mx is the exponent of that power of li.e base which is equal to Nm ; hence PROPERTY III. **The logarithm of any power of a number is equal to the** logu rilhm of that number multiplied by the exponent of the power. EXAMPLES. Ex. 1. Find the third... | |
| John Hymers - Logarithms - 1858 - 320 pages
...diminished by that of the divisor. Since m — a", n = a", m a_ i fm\ ii .'' S" (n) = X~y= g" m ~ g° n' 9. **The logarithm of any power of a number is equal to the** product of the logarithm of the number by the index of the power. Since m = a", .: mr = (a*)" = a",... | |
| Elias Loomis - Logarithms - 1859 - 372 pages
...-0.4753 divided by -36.74. INVOLUTION BY LOGARITHMS. (14.) It is proved in Algebra, Art. 340, that **the logarithm of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we,... | |
| William Henry Johnstone - 1859 - 78 pages
...n, or x = loga m, y = loga я l ,vm ax then — = — = a'.v, n ae = \ogam-logan. 7. ln any system, **the logarithm of any power of a number is equal to the logarithm of** that number multiplied by the index of that power. Let a' — m, or x = loga m ¡ then m? — (a')'... | |
| Charles Davies - Algebra - 1860 - 414 pages
...the n'* power, we have, a«' = N'a ..... (5). But from the definition, we have, nx' — log (N'*) ; **that is, The logarithm of any power of a number is...the number multiplied by the exponent of the power.** 233. If we extract the nth root of both members of equation {1), we shall have, a" =(N')*= \fW - -... | |
| Charles Davies - Algebra - 1860 - 328 pages
...members of ( 3 ) to any power denoted by p, we have, Whence, by definition, px — Log mf . . . ( ?.) **That is, the logarithm of any power of a number is...logarithm of the number multiplied by the exponent of the** poicer. If we extract any root of both members of ( 3 ), denoted by r, we have, a' = Whence, by definition,... | |
| Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...ar» exponent equal to 3x5; thus, (a")i=ali, and, generally, (a")m=anm. Hence, the logarithm of the **power of a number is equal to the logarithm of the number multiplied by the exponent of the power.** To extract the 5th root of the number a', we write a, giving it an exponent equal to f ; thus, v/as=a?,... | |
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