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Math Help - Log Qn (Not too hard!!)

  1. #1
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    Log Qn (Not too hard!!)

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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by matty888 View Post
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    using the integral defintion of the natural log we get

    \ln(x)=\int_{1}^{x}\frac{1}{t}dt

    let u=t^{1/n} \iff u^n=t \to nu^{n-1}=dt

    \ln(x^n)=\int_{1}^{x^n}\frac{1}{t}dt=\int_{1}^{x}\  frac{1}{u^n}(nu^{n-1}du)=n\int_{1}^{x}\frac{1}{u}du=n\ln(x)
    Last edited by TheEmptySet; May 16th 2008 at 07:02 AM. Reason: typo in post
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    Thank you(Further Qn)

    TheEmptySet you are a lifesaver,I have one further question,could you tell me how the limits of integration change from 1 and x^n to 1 and u? I would be very grateful(I kinda know its to do with the fact that you made a substitution)!
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    Behold, the power of SARDINES!
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    Quote Originally Posted by matty888 View Post
    TheEmptySet you are a lifesaver,I have one further question,could you tell me how the limits of integration change from 1 and x^n to 1 and u? I would be very grateful(I kinda know its to do with the fact that you made a substitution)!
    u=t^{\frac{1}{n}} or u as a function of t

    u(x^n)=t^{\frac{1}{n}} \to u(x^n)=(x^n)^{\frac{1}{n}}=x

    it is a typo. It should be x.

    I will fix the above post.
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