 | Elias Loomis - Trigonometry - 1855 - 192 pages
...the seventh power of 0.8952. EVOLUTION BY LoGARITHMS. (15.) It is proved in Algebra, Art. 341, that the logarithm of any root of a number is equal to the logarithm of that numoer divided by the index of the root. Hence, to extract the oot of a number by... | |
 | Benjamin Peirce - Algebra - 1855 - 308 pages
...substitute p — ran, in the above equation, it becomes log. p = n log. v/ p, log. v P = k*Z; n that is, the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. 13. Corollary. • The equation log. m... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...shall have, , a" -(N')~n- *JW - - (6). But from the definition, yj — — log ( n-/N') ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. 234i From the principles demonstrated in... | |
 | William Henry Johnstone - 1859 - 80 pages
...power. Let a' — m, or x = loga m ¡ then m? — (a')' or loga (m') = tx = ílogam. 8. ln any system, the logarithm of any root of a number is equal to the logarithm of that number divided by the index of that root. Let ax = m, ОГ X = loga m ; J 1 then(m)'=(a')7... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...equation {1), we shall have, a" =(N')*= \fW - - (6). But from the definition, — = log ("yF) ; that is, The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. 234i From the principles demonstrated in... | |
 | Henry Lee Scott - History - 1861 - 674 pages
...a number is equal to the product of the logarithm of the number by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. These properties of logarithms greatly facilitate... | |
 | James Hamblin Smith - 1869 - 412 pages
...logarithm of the number and the index denoting the power. Let m = a*. Then mr = a" = r . log m. 374. The logarithm of any root of a number is equal to...denoting the root. Let m = a*. I £ Then m' = a'; — У .-. logmr = = - . log m. 375. Since log mn = log m + log n, we can find the logarithm of any... | |
 | James Hamblin Smith - Algebra - 1870 - 452 pages
...proceed thus, log 13= 1-1139434 4 4-4557736 which is the logarithm of 28561, the number required. 458. The logarithm of any root of a number is equal to...of the number by the number denoting the root. Let m=a'. i » Then mf=aT; I x :. logamr = = -.logawi. Thus the operation of Evolution is changed into... | |
 | James Hamblin Smith - Algebra - 1870 - 478 pages
...which is the logarithm of 28561, the number required. 458. The logarithm of any root of a number ii equal to the quotient arising from the division of...the number by the number denoting the root. Let m = ax. Then mf=af; = -.loga»i. Thus the operation of Evolution is changed into Division. If, for example,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...the seventh power of 0.8952. EVOLUTION BY LOGARITHMS. (15.) It is proved in Algebra, Art. 341, that the logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. Hence, to extract tfot -cot of a number... | |
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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. 
