# How do you graph sqrt(ln x) ?

Feb 16, 2016

See the graph drawn below

#### Explanation:

1. $\ln 0$ 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 $\ln x$ is negative for all values of $x < 1$, as square root of given function is real only for $x \ge 0$.

3. Hence point $\left(1 , 0\right)$ 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]}