  Exploiting a recently constructed target space action for the exact string
black hole, logarithmic corrections to the leading order entropy are studied.
There are contributions from thermal fluctuations and from corrections due to
alpha'>0 which for the microcanonical entropy appear with different signs and
therefore may cancel each other, depending on the overall factor in front of
the action. For the canonical entropy no such cancellation occurs. Remarks are
made regarding the applicability of the approach and concerning the
microstates. As a byproduct a formula for logarithmic entropy corrections in
generic 2D dilaton gravity is derived.
