Erase the space in assigment operator.
array_var[$x]=`expr $base_val + $x`
Erase the space in assigment operator.
array_var[$x]=`expr $base_val + $x`
Depending on which shell you are using and the value of x, that syntax may work. ksh supports arrays.
Better use of ksh would be:
array_var[x]=((base_val + x))