Math Help - Can this be simplified?

1. Can this be simplified?

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!

2. In general, no. ln(x+ y) does not simplify.

3. As HallsofIvy has said, you can't simplify anything outside the logarithm. However, if you know how many times you've got $z = 0$ (say, $n$), and how many times you've got $z = 1$ (say, $m$), then you can simplify inside the logarithm thus:

$\ln(n + m e^{\theta}).$

That's the end of the road, however.