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

1. ## 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)

2. $\displaystyle \displaystyle F(x)= \ln (x)+C$

$\displaystyle \displaystyle F(1)= 2$

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

$\displaystyle \displaystyle \ln (1)+C= 2$

$\displaystyle \displaystyle 0+C= 2$

$\displaystyle \displaystyle C= 2$

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

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