# An Elementary Treatise on Logarithms: With Tables of the Logarithms of Numbers and Trigonometrical Functions

R. S. Davis & Company, 1878 - Logarithms - 96 pages
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Page 5 - If the number is greater than 1, the characteristic is one less than the number of figures to the left of the decimal point.
Page 10 - This table is added simply for convenience, as the same mantissas are to be found in the rest of the table. To find the logarithm of any number consisting of four figures. Find, in the column headed N, the first three figures of the given number. Then the mantissa of the required logarithm will be found in the horizontal line corresponding, in the vertiral column which has the fourth figure of the given number at the top.
Page 7 - The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Assume the equations 10*=ml; whence, {^«gm.
Page 6 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors.
Page 29 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.
Page 3 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a
Page 11 - From the table, we find log 3296 = 3.517987 log 3297 = 3.518119 That is, an increase of one unit in the number produces an increase of .000132 in the logarithm. Then evidently an increase of .78 unit in the number will produce an increase of .78 x .000132 in the logarithm = .000103 to the nearest sixth decimal place.
Page 3 - ... 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 ofthat number. Thus, if a be the base of a system of logarithms, and a? = N, then 2 is the logarithm of N...
Page 4 - We see, that in the common system, the logarithm of any number between 1 and 10, is found between 0 and 1. The logarithm of any number between 10 and 100, is...