Point closest to a curve

Let a curve be the graph of $f(x)$ and $P$ some fixed point.

What is the minimum distance between $P$ and a point $Q$ on the curve?

$f(x) = \log_e(x)$, $\quad x > 0$

$P = (1,1)$, $Q=(x, f(x))$ with $x$ given by:

$x =$ 1.0