= Solution
Use a <Tully-Fisher relation> $L\propto v_{\max}^4$. A simple justification assumes comparable mean surface brightness, so $L\propto R^2$, and comparable total <mass-to-light ratio>, so $M\propto L$. The virial scaling $v^2\sim GM/R$ then gives $v^4\propto M^2/R^2\propto L$. Calibrating to the previous galaxy yields
$$
\boxed{L_2\simeq1.47\times10^{10}\left(\frac{100}{269.6}\right)^4L_{V,\odot}\simeq2.79\times10^8L_{V,\odot}.}
$$
This is a rough luminosity estimate: the empirical slope depends on passband and population, and the assumed constant surface brightness and mass-to-light ratio are approximations rather than exact properties of every spiral galaxy.
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