 | Charles Davies - Surveying - 1839 - 376 pages
...Sines, ........ 37 but since a is the base of the system, m+n is the logarithm JlfxJV; 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... | |
 | Charles Davies - Surveying - 1839 - 376 pages
...member, we have but since a is the base of the system, ro+n is the logarithm ^/xJV; 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... | |
 | John Radford Young - 1839 - 332 pages
...Therefore n times the logarithm of any number is the logarithm of its nth power. THEOREM 2. The difference of the logarithms of any two numbers is equal to the logarithm of their quotient. For since a" = b, and a"' = c, by dividing, — = a*"1' = -, that is, x — x' — log. -.... | |
 | Charles Davies - Navigation - 1841 - 414 pages
...member, we have but since a is the base of the system, m+n is the logarithm JJ/xJV; 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... | |
 | Charles Davies - Algebra - 1842 - 284 pages
...logarithms of any two numbers equal ? To what then, will the addition of logarithms) correspond ? 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. 177. If we... | |
 | Charles Davies - Algebra - 1848 - 300 pages
...logarithms of any two numbers equal ? To what then, will the addition of logarithms correspond ? 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. 177. If we... | |
 | James Thomson - 1848 - 326 pages
...logarithms of numbers are other numbers depending on them, and characterized by the property, that the sum of the logarithms of any two numbers is equal to the logarithm of their product. Thus, log 6+log c=log (6c). Hence also, since b=-.c, it follows, that c log6=log-+logc; whence log... | |
 | John Radford Young - 1851 - 266 pages
...so that m times the logarithm of a number is the logarithm of its »rath power. 1 19. The difference of the logarithms of any two numbers is equal to the logarithm of their quotient. For ?L=a'-x'=— .: x — a;'=log — ; that is, logn — logи'= af n' n' log — . Hence,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Multiplying equations (1) and (2), member by member, we have, or, m + n=log (Mx N); hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product. 4. Dividing equation (1) by equation (2), member by member, we have, mn MM 10 -=_r~0r, ra — tt =... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...equations (1) and (2), member by member, we have lO"""" = MxN or, m+n — log MxN : hence, The sum of the logarithms of any two numbers is equal to the logarithm of their productDividing equation (1) by equation (2), member by member, we have " ,m— n M ' M 10 = — or,... | |
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JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product. 
