= Solution
Set
$$
\theta=\frac{\mu+\frac12\sigma^2-r}{\sigma}
$$
and define $Q$ on $\mathcal F_T$ by
$$
\frac{dQ}{dP}
=\exp\left(-\theta W_T-\frac12\theta^2T\right).
$$
The <Cameron-Martin theorem for a linear drift> says that
$$
W_t^Q=W_t+\theta t
$$
is a <Brownian motion> under $Q$. Therefore
$$
S_t=S_0
\exp\left(\left(r-\frac12\sigma^2\right)t+\sigma W_t^Q\right).
$$
The discounted stock is an exponential Brownian martingale, so $e^{-rt}S_t$ is a $Q$-martingale. Thus $Q$ is a <Risk-neutral measure for the Black-Scholes model>.
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