PUBLISHED BY HARPER & BROTHERS

NO. 82 CLIFF-STREET.

DESCRIPTION

OF

THE TABLES.

1. LOGARITHMS of numbers are the indices that denote tho different powers to which a given number must be raised to produce those numbers.

2. If a be the given number, whose indices and powers are to be considered, then a£* being put equal to n, a, the given

number, or root, is called the base of the system of logarithms, Sin the number whose logarithm is considered, and Ex, the logarithm of that number.

3. Any number, except 1, may be taken for the base of a
system of logarithms. In the system in general use, the base
Xis 10; and this system affords the greatest facilities in calcula-

tions, because 10 is the base of the common numeration, both in
whole numbers and decimal fractions.

4. Taking a +=n, we have, Ex==log. n; and putting a+=
m, gives, iy=log. m. If the equations, ar=n, and ay=m, be
multiplied together, member by member, we have, ar Xay=
n Xm, or aety=n X m. In this expression, x+y is the loga-
rithm of nxm (2); from which we conclude, that the sum of
the logarithms of any two numbers, is equal to the logarithm of
their product.

5. If the equations aʻ=n, a!=m, be divided, member by meniber, ; or at

In this expression, x-y is the

ac

n

n

1 1694

ay

m

m

m

logarithm of (2); from which we conclude, that the difference of the logarithms of any two numbers, is equal to the logarithm of their quotient.