Answer
$ 2x-z=2$
Work Step by Step
As we are given that $\ln(x^2+y^2)-z=0$
Since, we have the vector equation $r(x,y,z)=r_0+t \nabla f(r_0)$
The equation of the tangent line for $\nabla f(1,0,0)=\lt 2,0,-1 \gt$ is
$2(x-1)+0(y-0)-1(z-0)=0$
or, $2x-2-z=0$
or, $ 2x-z=2$
