When does $F(x)=\ln x -1$ cut through the $x$ axis?

Question

If you differentiate this $F(x)=\ln x -1$ you will get $(1/x)$ right?

And how am I supposed to get $(e,0)$?

Answer 1

Consider x = 0, at this point ln(o) is undefined, but you are really solving for ln(x) = 1, and the only thing that fits the bill is taking x to be e, which gives your solution as the coordinate (e,0)

Answer 2

What you have to do is to solve the following equation:

$$F(x) = \ln(x) - 1 = 0.$$

When you do, you'll find out that $x = e$.

This is where the function crosses the $x$-axis. Thus, the point is $(e,0)$.