 | William Henry Johnstone - 1859 - 80 pages
...¡ 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 or loga\m -\ x ')= 7 1 — . logam. 9.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...both sides to the mth power, we have Mm = (a*)i" = a™ . ' Therefore, log (Mn) =xm= (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art.... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...sides to the with power, we have M ™ = (a*)~ = a** . Therefore, log (M m) = xm = (log M ) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...the with power, we have Mm = (a*)m = a™ . Therefore, log (Mm) = xm = (log M ) X m12. The logariihm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...to the rath power, we have M m = (a x ) m = a™ . Therefore, log (M m ) — xm = (log M) X ™. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...both sides to the mth power, we have Mm = (a*)"1 = a™ . Therefore, log (Mm) = xm = (log M) X m. 12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art.... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...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 by logarithms, we have the following RULE. Divide the logarithm... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...ax = m to any power p, we have a?* = mP, in which xp is the logarithm of m raised to the power p. 6. The logarithm of the root of any number is equal to...logarithm of that number divided by the index of the root. For, extracting the rth root of both members of the equation a1 — m we have in which * is the logarithm... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art.... | |
 | Benjamin Greenleaf - 1879 - 346 pages
...of =zm, and raising both members to the power p, we have <ff = mp, in which xp = loga m f. 361 • The logarithm of the root of any number is equal to the logarithm of the number, divided by the index of the root. For, assume the equation, c?= m, and extracting the rth... | |
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The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 
