In general, no. ln(x+ y) does not simplify.
I cant figure out how to simplify the following equation, but have been told it is possible:
ln(sum(e^(theta*z)))
In this case z is a discrete random variable that only takes on values of 1 or 0 because it comes from a bernoulli distribution. Theta is a value that will later become maximized. How can I simplify this? I know that since z is a discrete random variable that changes some things. Thanks!
As HallsofIvy has said, you can't simplify anything outside the logarithm. However, if you know how many times you've got (say, ), and how many times you've got (say, ), then you can simplify inside the logarithm thus:
That's the end of the road, however.