I have a slide on which there is written that under Black-Scholes model:

$$\ln S\_{T} \sim N \left ( \ln S\_t - \frac{1}{2}\sigma^2(T-t), \sigma^2(T-t) \right )$$

Now, [here](https://quant.stackexchange.com/questions/7811/in-black-scholes-why-is-log-fracs-t-triangle-ts-t-sim-phi-mu) there is a good explanation on why:

$$\ln{\frac{S\_{T}}{S\_t}} \sim N\left ((\mu - \frac{1}{2}\sigma^2)(T-t), \sigma^2 (T-t) \right )$$

but this did not solve my problem. In fact I cannot see how one can get from the second equation to the first one. I think that there is something wrong. Am I right?