 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...root multiplied by the index of the power, and 4th. The logarithm of any root of a number is cqidl to the logarithm of that number divided by the index of the root. On these four properties the following rules arc founded. TABLES OF LOGARITHMIC SINES, TANGENTS, of... | |
 | Robert Gibson - Surveying - 1833 - 436 pages
...of the equation ax=n, x- I x 1 be taken, then, am=nm; but- is the logarithm of nm; from 771 which h appears, that the logarithm of the, root of any number,...logarithms be positive or negative. These results show,-that the addition of logarithms corresponds to the multiplication of their numbers ; the subtraction... | |
 | Logarithms - 1836 - 192 pages
...the equation ax = n, - - ix . be taken, then, am = rem; but- is the logarithm of nm ; from m -- • which it appears, that the logarithm of the root of...These results show, that the addition of logarithms correspondí to the multiplication of their numbers ; the subtraction of logarithms, to the division... | |
 | William Chauvenet - Binomial theorem - 1843 - 102 pages
...of the power; the product is the logarithm of the required power. 63. The logarithm of any root of a number is equal to the logarithm of that number divided by the index of the root. For to extract the nth root of the equation a1-**— ft, we divide the exponents of each member by... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...according to the definition, - is the logarithm of N" ; that is to say, . 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 of logarithms. The logarithm of 81 is 1.908485... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...according to the definition, - is the logarithm of N" ; that is to say, 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 of logarithms. The logarithm of 81 is 1.908485... | |
 | Henry Law - Logarithms - 1853 - 84 pages
...m, is equal to n times the lugar rithm of m. PROPOSITION P. THEOREM. The logarithm of any root of a number, is equal to the logarithm of that number, divided by the exponent of the root. Let X = log;, m, then m = 6X ; let the square root of m = x, and the logarithm... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...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 of logarithms The logarithm of 81 is 1.908485... | |
 | 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.... | |
 | 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... | |
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The logarithm of any root of a number, is equal to the logarithm of that number divided by the index of the root. 
