Question

(x/2)^(1/2)>ln (x)

Answer 1

\[\sqrt{x/2}>\ln x\]
\[\sqrt{x/2}-\ln x>0\]
\[\ln e ^{\sqrt{x/2}}-\ln x>0\]
\[\ln (e ^{\sqrt{x/2}}/x)>0\]
x is only define when x is positive or 0
\[e ^{\sqrt{x/2}}/x\]is always greater than 1 if x is never negative
\[x \in \mathbb{R}, x \ge0\]