  We prove existence of renormalized solutions to general nonlinear elliptic
equation in Musielak-Orlicz space avoiding growth restrictions. Namely, we
consider \begin{equation*} -{\rm div} A(x,\nabla u)= f\in L^1(\Omega),
\end{equation*} on a Lipschitz bounded domain in $\mathbb{R}^N$. The growth of
the monotone vector field $A$ is controlled by a generalized nonhomogeneous and
anisotropic $N$-function $M $. The approach does not require any particular
type of growth condition of $M$ or its conjugate $M^*$ (neither $\Delta_2$, nor
$\nabla_2$). The condition we impose is log-Holder continuity of $M$, which
results in good approximation properties of the space. The proof of the main
results uses truncation ideas, the Young measures methods and monotonicity
arguments.
