#### Answer

$2=\sqrt {x-y}-\ln z$

#### Work Step by Step

Here, the level curve for $f(x,y,z)=\sqrt {x-y}-\ln z$ has the form of $c=\sqrt {x-y}-\ln z$
Also, $x=3,y=-1,z=1$
This implies that $c=\sqrt {3-(-1)}-\ln (1)$
or, $c=2 $
Hence, $c=\sqrt {x-y}-\ln z \implies 2=\sqrt {x-y}-\ln z$