| 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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