INDETERMINATE COEFFICIENTS. (28.) If a + a ̧x + a ̧x2 + &c. = b + b1x + b2x2 + &c. for every value of x, then (29.) Theory of logarithms, and logarithmic tables. (E. 220—55; Bour. 209-24.) Let log a represent the logarithm of a to any base; This is only a particular case of the following more general theorems, which may be demonstrated in a similar manner : whatever may be the form or value of u,, then Either of these equations may be taken as the definition of a logarithm: the former is most usually adopted; and the various properties are therefore given in the order in which they most naturally follow on that supposition. log x1+log x2+ log x, + &c. = log (x1. x. x3. &c.) 2 2 It will be hereafter seen that unity has an infinite number of logarithms, of which the above is the only possible one. |