We study logarithms of the form $\ln(m_q/m_b)$ which arise in
the inclusive semileptonic decay of a bottom quark to a quark of
mass $m_q$. We use the renormalization group to resum the
leading radiative corrections to these terms, of the form
$m_q^2\alpha_s^n\ln^n(m_q/m_b)$,
$m_q^3\alpha_s^{n+1}\ln^n(m_q/m_b)$ and
$m_q^4\alpha_s^n\ln^{n+1}(m_q/m_b)$. The first two resummations are trivial,
while the latter involves a non-trivial mixing of four-fermi operators in the
$1/m_b$
expansion. We illustrate this technique in a toy model in which the
semileptonic decay
is mediated by a vector interaction, before treating the more complicated case
of
left-handed decay.