I'm trying to write a gamma log likelihood function... and am stuck with taking the log of e^-x/theta..
Are the rules for taking the log of base e raised to a rational exponent i.e. x/theta, the same as -x/theta?
so, would taking the log of e raised to -x/theta be -x/theta ?
The reason i ask, is that I have seen elsewhere on the web that taking the log of this results in theta * sum(x), and i'm not entirely sure as to why this is.
Any help would be much appreciated!