Answer
$$\ln 5$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( {2,0, - 1} \right)} \ln \left( {2x + y - z} \right) \cr
& {\text{Using the limit laws }} \cr
& = \ln \left( {\mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( {2,0, - 1} \right)} \left( {2x} \right) + \mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( {2,0, - 1} \right)} \left( y \right) - \mathop {\lim }\limits_{\left( {x,y,z} \right) \to \left( {2,0, - 1} \right)} \left( z \right)} \right) \cr
& {\text{Evaluating the limit}}{\text{, substitute 2 for }}x,\,\,0{\text{ for y and }} - 1{\text{ for }}z \cr
& = \ln \left( {2\left( 2 \right) + 0 - \left( { - 1} \right)} \right) \cr
& {\text{simplifying}} \cr
& = \ln \left( {4 + 1} \right) \cr
& = \ln 5 \cr} $$
