...system of logarithms, all numbers are considered as the powers of some one number, arbitrarily assumed, which is called the base of the system ; and the exponent of that ftouw of the base, which is equal to any given number, is called Out LOGARITHM of that number. Thus,...

...(a')5=a15, $ If some number, arbitrarily assumed, be taken as a base, then The LOGARITHM of any number is the exponent of that power of the base, which is equal to that number. G2=N, a3=N', a*=W, then, 2, 3, and x are called the logarithms of N, N', and N", in the...

...and that they will be pronounced sufficiently extensive for all purposes of academic and colleglife instruction, as well as for practical mechanics and...called the logarithm of that number. The base of the cqmmon system of logarithms (called, from their inventor, Briggs' logarithms) is the number 10. Hence...

...square root of x+y , each member, we have a 2 = Vmn. Therefore, is the A logarithm of Vmn, since it is the exponent of that power of the base which is equal to Vmn. Now, in Briggs's system, the logarithm of 10 is 1, of 100 is 2, etc. Hence the logarithm of VlO...

...the lahor of Multiplication and Division, by substituting in their stead Addition and Subtraction. All numbers are regarded as powers of some one number,...the common system of logarithms (called, from their inventor, Briggs' logarithms) is the number 10. Hence all numbers are to be regarded as powers of 10....

...(2.) Therefore, according to the definition of logarithms, x+y is the logarithm of mn, since it is the exponent of that power of the base which is equal to mn. For convenience, we will use log. to denote logarithm, and we have x+y=log. mn=log. m + log. n....

...diminish the labor of multiplication and division by substituting in their stead addition and subtraction. All numbers are regarded as powers of some one number,...called the base of the system ; and the exponent of the power to which the base must be raised in order to be equal to a given number is called the logarithm...

...the labor of Multiplication and Division, by substituting in their stead Addition and Subtraction. All numbers are regarded as powers of some one number,...exponent of that power of the base which is equal toa given number is called the logarithm of that number. The base of the common system of logarithms...

...diminish the labor of multiplication and division by substituting in their stead addition and subtraction. All numbers are regarded as powers of some one number, which is called the base of the system ; and thl exponent of the power to which the base must be raised in order t: be equal to a given number is...

...which thus becomes the base of a logarithmic sytem. Moreover, the logarithm of any given number is the exponent of that power of the base which is equal to the given number. It is manifest that we sec here a return to involution; any number by its own self-involution...