 | Encyclopedias and dictionaries - 1823 - 856 pages
...logarithms of all numbers within certain limits may be applied to simplify calculations ; for since the sura of the logarithms of any two numbers is equal to the logarithm of their product, it follows, that as often as we have occasion to find the product of two or more numbers, we have only... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...exponent X — Z of the power of which a is the base, is the logarithm of -¡ : whence the difference of the logarithms of any two numbers is equal to the logarithm of their quotient. QED Theorem 3. — The logarithm of the nth power of any number * is equal to n times the... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...powers of J +a, the numbers S, 4, 5, &.c., for the same reasons, will fall into the series. 6. The sum of the logarithms of any two numbers is equal to the logarithm of the product of the same two numbers. Thus if 1 +a raised to the wth power be equal to the number N,... | |
 | Thomas Curtis (of Grove house sch, Islington) - 412 pages
...-)- г1 — abf but r* X г1 = г* +1» therefore A -f В is the logarithm of ah ; that is, the sum of the logarithms of any two numbers is equal to the logarithm of the product. Again -5- = т-; but -p — r * "; therefore, A— R is the logarithm of — ; that is,... | |
 | Charles Davies - Surveying - 1830 - 318 pages
...nXwz. In this expression, x+y is the logarithm of n X m (2) ; from which we conclude, that tht sum of the logarithms of any two numbers, is equal to the logarithm of their product. ri. If the equation* ar=n, a»=m, be divided, member by member, - =- ; or oI~*=-. In this expression,... | |
 | Charles Davies - Surveying - 1830 - 390 pages
...expression, a: — w is the o» mm logarithm of - (2) ; from which we conclude, that, the difference of tfie logarithms of any two numbers, is equal to the logarithm of their quotient. 6. If in the equation az=n, both members be raised to the mth power, a™z=nm. Here, mx is... | |
 | John Radford Young - Algebra - 1832 - 408 pages
...either accurately found, or may be approximated to, to any degree of precision. (6.) THEOREM 1. The sum of the logarithms of any two numbers is equal to the logarithm of their product. Let b be any number, and let its logarithm be x ; and let с be any other number, whose logarithm is x' ;... | |
 | Robert Gibson - Surveying - 1833 - 436 pages
...«I+!'=nXm. In this expression, x+y is the logarithm of reX»i (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 ax=n, t&=^m, be divided, member by member, — =-; or ax~~y=-. In this expression,... | |
 | Charles Davies - Navigation - 1837 - 342 pages
...by member, we have but since a is the base of the system, m+n is the logarithm MxN; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers. 3. If we... | |
 | Euclides - 1838 - 264 pages
...of addition and subtraction. ' The two theorems which follow make this manifest. THEOREM I. The sum of the logarithms of any two numbers is equal to the logarithm of the product of those fc numbers. Let N be any number, and ,c its logarithm ; that is, let 10* = N ;... | |
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JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product. 
