On Generalized Logarithmic Electrodynamics

The generalized logarithmic electrodynamics with two parameters $\beta$ and $\gamma$ is considered. The indexes of refraction of light in the external magnetic field are calculated. In the case $\beta =\gamma$ we come to results obtained by P. Gaete and J. Helay"el-Neto [7] (Eur.Phys.J. C$\mathbf{\text{74}}$, 2816 (2014)). The bound on the values of $\beta$, $\gamma$ was obtained from the Bir'efringence Magn'etique du Vide (BMV) experiment. The symmetrical Belinfante energy-momentum tensor and dilatation current are found.