 | Benjamin Greenleaf - 1862 - 518 pàgines
...(a x ) m = a"" . ' Therefore, log ( M m ) = xm— (log M) X m. 12. The logarithm of the BOOT 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. 9) Therefore, log x loa M 13. Hence, by means... | |
 | Benjamin Greenleaf - 1861 - 638 pàgines
...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. 9) Therefore, log WM) = -= - fe —. 1 ,mt—\... | |
 | Benjamin Greenleaf - 1863 - 502 pàgines
...(a x ) m = 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. 9) Therefore, log 13. Hence, by means of logarithms,... | |
 | Benjamin Greenleaf - 1863 - 504 pàgines
...(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. 9) . M = a x , then, extracting the nth. root... | |
 | Charles Davies - 1863 - 338 pàgines
...3 ), denoted by r, we have, 01 a' = Whence, by definition, = Log (8.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by tlie index of the root. The applications of the above principles require a table of logarithms. A TABLE... | |
 | Aaron Schuyler - 1873 - 508 pàgines
...the' fifth power of .9. Ana. .59047. EVOLUTION BY LOGARITHMS. 25. Proposition. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let (1) b*~n; then, by def., log n~x. V/Cl) = (2) ft? =\/~n; then, by def., log V^ = - ",•— log... | |
 | Benjamin Greenleaf - 1864 - 420 pàgines
...rth power, we have m r = (<f) r = a*". Therefore, log (TO') = xr = r log m. 402. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. For, let m = a' ; then, extracting the rth root of both members, we have 403. The arithmetical mean... | |
 | Charles William Hackley - 1864 - 532 pàgines
...by definition, — is the logarithm of N" ; that is to say, x i The logarithm of any root of a given number is equal to the logarithm of the number divided by the index of the root. Combining the last two cases, we shall find mx whence — is the logarithm of N". n It is of the highest... | |
 | Benjamin Peirce - 1864 - 314 pàgines
...above equation, it becomes • log. p = n log. v/ p, log. ^ p = fo*2; 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 ml = log. m + log. m', gives log. m' = log.... | |
 | Benjamin Peirce - 1864 - 298 pàgines
...becomes n log. p = n log. v/ p, or log. ^/ p = ——£_; n 1 "xl°ff- P that is, *Ae 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 m' = log. m -f- log. m', gives log. m' = log.... | |
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the logarithm of the m th root of a number is equal to the logarithm of the number divided by the index of the root LOGARITHMS. 
