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Math Help - Find a function F(x) such that F'(x)= 1/x and F(1)=2

  1. #1
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    Find a function F(x) such that F'(x)= 1/x and F(1)=2

    Find a function F(x) such that F'(x)= 1/x and F(1)=2 Leave an exact answer- do not approximate any numbers

    This is how I got it: To fine F(x) I found the antiderivative for F'(x).
    The antiderivative of 1/x is equal to ln(x), because the derivative of ln(x) is 1/x. I know that the derivative of log a (x) is equal to 1/(x ln(a)). So, in ln(x), the value of a is e. ln(e) is equal to 1, so finally, I know that the derivative of ln(x) is equal to 1/x, therefore the antiderivative of 1/x is equal to ln(x), because the derivative and the antiderivative are opposites of each other.

    F(x)= ln(x)
    Know that I know what F(x) is and that F(1)=2 what do I do next?

    F(1)=ln(1)=0 (so what about the 2- Thanks for the help)
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    \displaystyle F(x)= \ln (x)+C

    \displaystyle F(1)= 2

    \displaystyle F(1)= \ln (1)+C \implies \ln (1)+C= 2

    \displaystyle  \ln (1)+C= 2

    \displaystyle  0+C= 2

    \displaystyle  C= 2

    \displaystyle F(x)= \ln (x)+2
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