linear proportionality between L$_X$ and L$_{FIR}$ we find: $$Log L_X = Log L_{FIR} - 3.18
\label{XFIR}$$ with a $\sigma$ of 0.47, based on 147 galaxies. This relation is plotted as a dashed line in the right panels of Figures from \[X1\] to \[X3\].

We note that the B and FIR luminosities are also connected in late-type galaxies by means of a linear relation fitted by: $$Log L_{FIR} = Log L_B - 0.38$$ with a r.m.s.=0.5. This equation, inserted into the relation (\[XBlate\]) gives: $$Log L_X = Log L_{FIR} -3.47$$ similar to the result of equation (\[XFIR\]) and to that found by @ranalli. This is an independent way to confirm our results and to verify the existence of a global link between L$_{FIR}$, B light and X-ray emission. The connection between B luminosity or galaxy area and X or FIR luminosities will be discussed in Section \[Discussion\].

Early-type galaxies
-------------------

When the early-type galaxies are considered in the above described relations involving X-ray emission, the correlations become less evident. Considering soft X-ray and B luminosities, we find a relation: $$Log L_X = 2\  Log L_B - 13.57
\label{XBearly}$$ ($\sigma$=0.73) based on 224 galaxies and plotted as full line in Fig. \[X2\], 