| John Radford Young - 1839
...be convenient to establish the following characteristic properties of logarithms. (141.) 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... | |
| Charles Davies - 1839 - 261 sider
...member by 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.... | |
| Charles Davies - 1841 - 359 sider
...member by 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.... | |
| Charles Davies - 1842 - 258 sider
...the 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.... | |
| James Thomson - 1848
...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;... | |
| Charles Davies - 1848
...the 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.... | |
| John Radford Young - 1851
...as we shall see when a few obvious propositions in the theory of logarithms are stated. 1 1 7. Tne **sum of the logarithms of any two numbers is equal to the logarithm of** their product. Let a* = n, and a'—n' .: aI+•'=nn'; therefore, if a be the base of the system of... | |
| A. M. LEGENDRE - 1852
...shall have, 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,... | |
| Charles Davies, Adrien Marie Legendre - 1854 - 432 sider
...Multiplying equations (1) and (2), member by member, we have, 10m+ n = Mx N 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, JO™ »BB_OTjW_Wesi0g—... | |
| Charles Davies - 1854 - 322 sider
...Multiplying equations (1) and (2), member by member, we have, Wm + n = MxN OT,m + n=log(MxN); 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, 10m~n = -^or, m... | |
| |