 | Elias Loomis - 1855 - 356 σελίδες
...shall obtain X therefore, according to the definition, — is the logarithm of i N"; hence PROPERTY IV. The logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. EXAMPLES. Ex. 1. Find the square root of 81 by means... | |
 | Joseph B. Mott - 1855 - 58 σελίδες
...n 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 =... | |
 | Charles Davies - 1857 - 408 σελίδες
...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 the four preceding • articles, we deduce... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 σελίδες
..._. 10" =M~a' ± in which - is the logarithm of M" : that is, n The logarithm of the root of a given number is equal to the logarithm of the number divided by the index of the root. EXAMPLES. 1. What is the 5th power of 9? Log 9 = 0.954243 ; 0.954243 X 5 = 4.771215;... | |
 | John Hymers - 1858 - 324 σελίδες
...where r is any number whole or fractional, positive or negative. 10. The logarithm of the root of any number is equal to the logarithm of the number divided by the index of the root. Since m = a", .: log„ (Jm) = ^ = — (log.«»). 11. Hence, if we have to multiply... | |
 | William Henry Johnstone - 1859 - 80 σελίδες
...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 or... | |
 | Charles Davies - 1860 - 412 σελίδες
...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 the four preceding articles, we deduce... | |
 | Henry Lee Scott - 1861 - 674 σελίδες
...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 arithmetical operations. For if... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...™ = (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) 1 ,mt—\ x log Af Therefore,... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...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. 9) Therefore, log 13. Hence,... | |
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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. 
