# Thread: Logarithm of base e raised to rational exponent

1. ## Logarithm of base e raised to rational exponent

Hi All,

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!

Thanks guys!!!

2. Originally Posted by sjohri214
Hi All,

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!

Thanks guys!!!
yeah you are right

3. Originally Posted by sjohri214
Hi All,

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!

Thanks guys!!!
yes, $\ln e^x = x$. x can be rational, doesn't matter

4. Thanks for your replies guys!