 | Elias Loomis - Calculus - 1851 - 296 pages
...preceding Proposition, da*=a* log.' a.dx. Put M=a% and we find du dx= — ; - — . u log.' a If a be the base of a system of logarithms, then x is the logarithm of u in that system, and j — ; — , Algebra, Art. 349, is the modulus of the system, which we will... | |
 | Elias Loomis - Calculus - 1859 - 320 pages
...preceding Proposition, <fa*=aI log.' a.dx. Put u— a't and we find du dx——. - — . u log.' a If a be the base of a system of logarithms, then x is the logarithm of u in that system, and = — - — , Algebra, Art. 349, is the modulus of the system, which we will... | |
 | Mathematics - 1874 - 430 pages
...substituting u for ax, dx = du (7) Therefore, (7) is the differential of the logarithmic function (6). If a is the base of a system of logarithms, then x is the logarithm of u in that system and 1-f-loga is the modulus of the system. Therefore, if we represent 1 -=- log a,... | |
 | Electronic journals - 1874 - 490 pages
...= — , a" log au log a Therefore, (7) is the differential of the logarithmic function (6). If a is the base of a system of logarithms, then x is the logarithm of u in that system and 1 -*- log a is the modulus of the system. Therefore, if we represent 1 -±- log... | |
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M=a% and we find du dx= — ; - — . u log.' a If a be the base of a system of logarithms, then x is the logarithm of u in that system, and j — ; — , Algebra, Art. 