 | Elias Loomis - Algebra - 1855 - 356 pages
...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... | |
 | 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 logarithms,... | |
 | Joseph B. Mott - Algebra - 1855 - 58 pages
...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 - 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...logarithm of the number divided by the index of the root. 234i From the principles demonstrated in the four preceding • articles, we deduce the following practical... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
..._. 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; whole number answering... | |
 | John Hymers - Logarithms - 1858 - 324 pages
...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 two numbers together,... | |
 | 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 or... | |
 | 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...logarithm of the number divided by the index of the root. 234i From the principles demonstrated in the four preceding articles, we deduce the following practical... | |
 | 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...logarithm of the number divided by the index of the root. These properties of logarithms greatly facilitate arithmetical operations. For if multiplication is... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...™ = (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, log WM ) = -=... | |
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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. 
