No, the given system is not linear. A linear system should satisfy the properties of homogeneity and additivity.
1. To determine if a system is linear, we need to check two conditions: homogeneity and additivity.
2. Homogeneity: A system is homogeneous if scaling the input by a constant scales the output by the same constant. In this case, scaling x by a constant will scale both the 2x[-1] term and the log(x) term, resulting in a non-linear relationship.
3. Additivity: A system is additive if the sum of two inputs produces the sum of the corresponding outputs. However, in this case, adding two inputs x1 and x2 will result in the addition of both the 2x[-1] terms and the log(x) terms, leading to a non-linear relationship.
4. Therefore, since the given system fails both the homogeneity and additivity conditions, it is not linear.
The complete question is:
Given