# Logarithm of base e raised to rational exponent

• Jul 15th 2008, 05:11 PM
sjohri214
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!!! (Wink)
• Jul 15th 2008, 05:13 PM
Mathstud28
Quote:

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!!! (Wink)

yeah you are right
• Jul 15th 2008, 05:15 PM
Jhevon
Quote:

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!!! (Wink)

yes, $\ln e^x = x$. x can be rational, doesn't matter
• Jul 16th 2008, 04:32 AM
sjohri214