Stock Price - Expectation Log of Stock Price

Question

One of stock price model is GBM, which is $$ dS_t = {\mu}S_tdt + {\sigma}S_tdW $$ with the solution of the model is $$ S_t = S_0e^{(\mu - \frac{\sigma^2}{2})t + {\sigma}W_t} $$ with $ ln(\frac{S_t}{S_0}) \sim N\Big{(}(r - \frac{1}{2}\sigma^2)t, \sigma^2t\Big{)} $ and $ r $ is risk-free interest rate.

I have several question

1. How to prove that $ \mathbf{E}\Big{(}ln(\frac{S_t}{S_0})\Big{)} = (r - \frac{1}{2}\sigma^2)t $?
2. Why $ \mu $ is equal to $ r $?

Note: I have succeeded to prove $ var\Big{(}ln(\frac{S_t}{S_0})\Big{)} = \sigma^2t$ by using induction.