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:<math>t = \log_b \frac{p}{1-p} = \beta_0 + \beta_1 x_1 + \beta_2 x_2+ \cdots +\beta_M x_M </math>
where ''t'' is the log-odds and <math>\beta_i</math> are parameters of the model. An additional generalization has been introduced in which the base of the model (''b'') is not restricted to the [[Euler's number]] ''e''. In most applications, the base <math>b</math> of the logarithm is usually taken to be ''[[E (mathematical constant)|e]]''. However, in some cases it can be easier to communicate results by working in base 2 or base 10.
For a more compact notation, we will specify the explanatory variables and the ''β'' coefficients as {{tmath|(M+1)}}-dimensional vectors:
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