  It is shown explicitly that the correlation functions of Conformal Field
Theories (CFT) with the logarithmic operators are invariant under the
differential realization of Borel subalgebra of $\W_\infty$-algebra. This
algebra is constructed by tensor-operator algebra of differential
representation of ordinary $sl(2,C)$. This method allows us to write
differential equations which can be used to find general expression for three
and four-point correlation functions possessing logarithmic operators. The
operator product expansion (OPE) coefficients of general logarithmic CFT are
given up to third level.
