Books Books The logarithm of any root of a number, is equal to the logarithm of that number divided by the index of the root. Elements of Surveying - Page 10
by Charles Davies - 1830 - 300 pages ## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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... ## The Theory and Practice of Surveying: Containing All the Instructions ...

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... ## A Table of Logarithms: Of Logarithmic Sines, and a Traverse Table

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... ## Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ...

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... ## A Treatise on Algebra

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... ## A Treatise on Algebra

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... ## Rudimentary Treatise on Logarithms

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... ## A Treatise on Algebra

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... ## An elementary Treatise on Logarithms

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.... 