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Math Help - Logarithm of base e raised to rational exponent

  1. #1
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    Cool 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!!!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by sjohri214 View Post
    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
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sjohri214 View Post
    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
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  4. #4
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    Thanks for your replies guys!
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