When ln() is taken to both sides of the equation it is supposed to simplify to:

I'm wondering by what rules was each side simplified. I know that ln(e) is 1 but in this case ln(e^k^t) is the quantity k*t? The fact that ln(1/2) simplifies somehow to -ln(2) just leaves me bewildered at this point.

Thanks in advance for any posts on this...