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Math Help - help with natural logarithm

  1. #1
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    help with natural logarithm

    question:

    ln(x^2)/ln(e^x)

    I just don't see anything on the formula sheet that matches this.

    List of integrals of logarithmic functions - Wikipedia, the free encyclopedia
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  2. #2
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    Re: help with natural logarithm

    I assume you wish to integrate this expression?

    \frac{\ln(x^2)}{\ln(e^x)}} = \frac{2\ln{x}}{x}

    \int 2\ln{x} \cdot \frac{1}{x} \, dx

    integration by substitution ...

    let u = \ln{x}

    can you finish?
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  3. #3
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    Re: help with natural logarithm

    Quote Originally Posted by togo View Post
    question:
    ln(x^2)/ln(e^x)
    What is the question? The above is a statement:

    \frac{\ln(x^2)}{\ln(e^x)}=\frac{2\ln(x)}{x}.
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  4. #4
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    Re: help with natural logarithm

    I don't see a question! You give an expression. What do you want to do with it? If you are trying to "simplify" it then two basic properties should help: ln(x^2)= 2ln(x) and [tex]ln(e^x)= x[/itex].

    You give a link to a "list of integrals". Do you want to integrate that? 2\int [ln(x)/x] dx? Then I think the substitution u= ln(x) will do nicely!
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    Re: help with natural logarithm

    want to integrate it.
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  6. #6
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    Re: help with natural logarithm

    yeah I have no idea where to find the rule for handling that. It didn't look like it was on the wikipedia formula sheet.
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  7. #7
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    Re: help with natural logarithm

    recommend you research the technique of integration by substitution
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  8. #8
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    Re: help with natural logarithm

    Quote Originally Posted by togo View Post
    yeah I have no idea where to find the rule for handling that. It didn't look like it was on the wikipedia formula sheet.
    ...
    Attached Thumbnails Attached Thumbnails help with natural logarithm-lnintegrals.png  
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    Re: help with natural logarithm

    Quote Originally Posted by skeeter View Post
    I assume you wish to integrate this expression?

    \frac{\ln(x^2)}{\ln(e^x)}} = \frac{2\ln{x}}{x}

    \int 2\ln{x} \cdot \frac{1}{x} \, dx

    integration by substitution ...

    let u = \ln{x}

    can you finish?
    Do you see how this sets you up quite nicely?
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  10. #10
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    Re: help with natural logarithm

    Quote Originally Posted by togo View Post
    yeah I have no idea where to find the rule for handling that. It didn't look like it was on the wikipedia formula sheet.

    What is the derivative of \left[\ln(x)\right]^2~?
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