...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 power of the base which is equal to any given number, is called the LOGARITHM of that number. In the common system of logarithms unity...

...numbers are confident site powers of some one number, arbitrarily assumed, which is called the BW' the system, and the exponent of that power of the base which is equal fc s; given number is called the LOGARITHM oftiial number. Thus, if a be the base of a system of logarithms,...

...в . •69897 . -77815 7 8 . -84510 . -90309 9 10 •95424 . 1-0000 In every system of logarithms, the exponent of that power of the base which is equal to 1, must be 0 ; for on tho principles which have just been shown to apply to the division of a power...

...^^^a 4 . 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. « 2 =N, a 3 =N', a I =N // , then, 2, 3, and x are called the logarithms of N, N x ,...

...^/V^a 4 . 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. G 2 =N, « 3 =N', «- c =N // , then, 2, 3, and X are called the logarithms of N, W, and...

...we have a px =m p . Therefore, according to the definition,^ is the logarithm of m p j since it is the exponent of that power of the base which is equal to m?. That is, Therefore, to involve a given number to any power, we multiply the logarithm of the number...

...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 power of the base which is equal to any given number, is called the LOGARITHM of that number. (9) The logarithm of a number consists of...

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

...exponent of that power of the base by the number which marks the degree of the root. The quotient will be the exponent of that power of the base which is equal to the root required. Thus, the 3d root of 4096 = 2", is 2*= 16; and the 5th root of 32768 = 2", ia2'...

...exponent of the power. Therefore, according to the definition, px is the logarithm of m p , since it is the exponent of that power of the base which is equal to W. That is, equal t( Therefore, to involve a given number to any power, we multiply the logarithm of...