= Solution
<Logistic regression> assumes independent $Y_i\mid X_i\sim\operatorname{Bernoulli}(\pi_i)$ with
$$
\log\frac{\pi_i}{1-\pi_i}=\beta_0+X_i^T\beta.
$$
For the binomial exponential family, $\ell=y\theta-m\log(1+e^\theta)+\text{constant}$, so the mean is $m e^\theta/(1+e^\theta)$ and the canonical parameter is its logit. It may be fitted by <iteratively reweighted least squares>.
Under LDA, Bayes' rule gives
$$
\log\frac{P(Y=1\mid x)}{P(Y=0\mid x)}=log\frac{\pi_1}{\pi_0}+(\mu_1-\mu_0)^T\Sigma^{-1}x- frac12(\mu_1^T\Sigma^{-1}\mu_1-\mu_0^T\Sigma^{-1}\mu_0),
$$
which is a logistic model with an intercept.
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