How do you graph ##sqrt(ln x) ##?

See the graph drawn below

1. ##ln0## is undefined. It's not a real number, because you can never get zero by raising anything to the power of anything else.

2. Also, function ##lnx## is negative for all values of ##x<1##, as square root of given function is real only for ##x>=0##.

3. Hence point ##(1,0)## lies on the graph and the graph does not exist for all values of ##x<1##

4. Graph increases as square root of a logarithmic for all positive values of ##x##

graph{y=(ln x)^(1/2) [-0.35, 9.104, -0.55, 4.18]}