Relative logarithmic order of an entire function

In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order $\rho _{g}^{l}(f)$ of a nonconstant entire function $f$ with respect to another nonconstant entire function $g.$ Next we investigate some theorems related the behavior of $\rho _{g}^{l}(f)$. We also define the relative logarithmic$ $proximate order of $f$ with respect to $g$ and give some theorems on it.