 | Joseph B. Mott - Algebra - 1855 - 58 pages
...log a ; T —Y and if n = -, then losam = - losa : m ° m that is, the logarithm of any power or root of a number is equal to the logarithm of the number multiplied by the exponent ....... , ------ ----------- --------- (THEOREMS.) 1. log 81 = log 34 = 4 log 3 = 4X. 477121 = 1.908484.... | |
 | Elias Loomis - Trigonometry - 1855 - 192 pages
...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 have... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...=x+l, log. 20000 = log. 2000=a;+3, log. 2000000=, &c. We have seen, in Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied bv the exponent of the power. Hence, log. 4 =2x, log. 32 = log. 16=4a;, log.... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...have, a*.' = N'n (5). But from the definition, we have, nx' — log (N/n) ; that is, The logarithm of any power of a number is equal to the logarithm...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')~n- *JW -... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...10mXn=J/n, in which m X n is the logarithm of M * (Art. 1) : hence, The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. 16. Taking the same equation, W'" = M, and extracting the nth root of both members, we have m _. 10"... | |
 | 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... | |
 | Elias Loomis - Logarithms - 1859 - 372 pages
...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 - 80 pages
...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 - 412 pages
...a«' = N'a ..... (5). But from the definition, we have, nx' — log (N'*) ; that is, The logarithm of any power of a number is equal to the logarithm...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 - 332 pages
...power denoted by p, we have, Whence, by definition, px — Log mf . . . ( ?.) That is, the logarithm of any power of a number is equal to the 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,... | |
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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. 
