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Math Help - Natural Log help

  1. #1
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    Natural Log help

    I'm stuck on this question;

    Suppose c is a number such that area(1/x,1,c)> 1000. Explain why c> 2^1000

    can someone clarify what natural log is for me?


    thank you so much (:
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  2. #2
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    Quote Originally Posted by dondonlouie View Post
    I'm stuck on this question;

    Suppose c is a number such that area(1/x,1,c)> 1000. Explain why c> 2^1000
    I assume by ‘area’ you mean \int_1^c {\frac{{dx}}{x}}  = \ln (c).

    So you want to solve \ln(c)>10^3. Recall that e^{\ln(c)}=c.
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  3. #3
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    Quote Originally Posted by Plato View Post
    I assume by ‘area’ you mean \int_1^c {\frac{{dx}}{x}}  = \ln (c).

    So you want to solve \ln(c)>10^3. Recall that e^{\ln(c)}=c.
    wouldn't it just be 1000?
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  4. #4
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    Quote Originally Posted by dondonlouie View Post
    wouldn't it just be 1000?
    No indeed!

    If \ln(c)>1000 then c>e^{1000}.
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