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How do you graph ##sqrt(ln x) ##?
See the graph drawn below

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

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

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

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]}