The complete solution of the partial differential equation \(\frac{{\partial z}}{{\partial y}} = \ln \left( {\frac{{\partial z}}{{\partial x}}} \right)\) will be 

1
z = ax - y ln a + c where a and c are arbitrary constants.
2
z = ax - (y/ln a) + c where a and c are arbitrary constants.
3
z = ax + y ln a + c where a and c are arbitrary constants.
4
z = ax + (y/ln a) + c where a and c are arbitrary constants.

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