  Part of the order $\alpha_s$ correction to the inclusive $B\to X_s\,\gamma$
photon spectrum is enhanced by $\log(m_b^2/m_s^2)$. We discuss its origin and
sum the corrections proportional to $[\alpha_s\log(m_b^2/\mu^2)]^n$ to all
orders. These are the calculable leading logarithms in the parton fragmentation
functions of a quark or gluon into a photon. Although the gluon fragmentation
into a photon starts only at order $\alpha_s^2$, its contribution is of the
same order as the $s$ quark's in the leading log sum. For not too small values
of the photon energy, the resummation yields a moderate suppression. In the
standard model, the coefficient of the operator whose matrix element gives rise
to such terms is small. A measurement of the photon spectrum around $1\,$GeV
would provide a theoretically clean determination of $C_8$, the Wilson
coefficient of the $b\to s\,g$ operator.
