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Math Help - Exponential Rules

  1. #1
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    Exponential Rules

    Good afternoon everybody...

    I need some help on the following - I'm sure it's simple, but I've totallk forgot how to do it...

    Say I wanted to take the exponential of the following (where a and b are constants).

    ln(a*x)^b

    which, is the same as

    b*ln(ax)^b

    what would be the result?

    I really appreciate your help on this - I have searched the web - I'm totally blank!
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  2. #2
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    skeeter's Avatar
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    Re: Exponential Rules

    \ln(ax)^b = b\ln(ax) = b(\ln{a} + \ln{x}) = b\ln{a} + b\ln{x}

    note that this relationship also works right to left ...
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  3. #3
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    Re: Exponential Rules

    Many thanks Skeeter, that was a great help - another question, if I may - along the same ilk...

    I have this:

    \ln(ax+b)^k+c

    Now, taking an exponential, do I get...

    \exp(\ln(ax+b)^k+c) = (ax+b)^k+\exp(c)

    I can't find any info on this rule anywhere

    Many thanks for your helo so far - reps for you :-)
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  4. #4
    Behold, the power of SARDINES!
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    Re: Exponential Rules

    Quote Originally Posted by MaverickUK82 View Post
    Many thanks Skeeter, that was a great help - another question, if I may - along the same ilk...

    I have this:

    \ln(ax+b)^k+c

    Now, taking an exponential, do I get...

    \exp(\ln(ax+b)^k+c) = (ax+b)^k+\exp(c)

    I can't find any info on this rule anywhere

    Many thanks for your helo so far - reps for you :-)
    Not quite you rule you are looking for is

    e^{x+y}=e^{x}e^{y}

    So you should end up with

    e^{\ln(ax+b)^k+c}=e^{\ln(ax+b)^k}e^{c}=(ax+b)^ke^{  c}
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